Reminder of the objectives given for the last evaluation

The aim of this project is the development of modern tools for multi-scale modeling in biological phenomena. During the period 2014-2017, the objectives we had fixed were to develop modern tools for multi-scale modeling of biological phenomena, as detailed hereafter:

1. Multi-scale modeling of erythropoiesis, the process of red blood cell production, in order to describe normal, stress, and pathological erythropoiesis, using mathematical and computational models. This led to:
2. Multi-scale modeling of the CD8 T cell immune response, in order to develop a predictive model of the CD8 T cell response, by confronting the model at different stages to in vivo-acquired experimental data;
3. Population dynamics modeling, with the aim to develop general mathematical tools to study them. The main tools we were using were structured equations, in which the cell population is endowed with relevant structures, or traits. We identified limitations in using these formalisms, this is why we started developing multi-scale approaches;
4. Modeling of Chronic Myeloid Leukemia (CML) treatment, using ordinary differential equations models. Our team had already developed a first model of mutant leukemic cells being resistant to chemotherapy. A next step would be to identify the parameters using experimental data;
5. Multi-scale modeling carried out on the basis of hybrid discrete-continuous models, where dissipative particle dynamics (DPD) are used in order to describe individual cells and relatively small cell populations, partial differential equations (PDE) are used to describe concentrations of bio-chemical substances in the extracellular matrix, and ordinary differential equations for intracellular regulatory networks (Figure 1). An emphasis would be made on developing codes that are both flexible and powerful enough to implement variants of the model, perform simulations, produce desired outputs, and provide tools for analysis; to do so:
6. We planned to contribute to a recent project named chronos, whose code (written in C++) represents heterogeneous populations of individual cells evolving in time and interacting physically and biochemically, and the objective is to make the code flexible enough to implement different formalisms within the same model, so that different components of the model can be represented in the most appropriate way;
7. Partial differential equations (PDE) analysis, with a focus on reaction-diffusion equations, transport equations (hyperbolic PDEs) in which the structure can be age, maturity, protein concentration, etc., with particular cases where transport equations are reduced to delay differential equations (DDE).

Comments on these objectives over the evaluation period

We have had strong contributions to objectives 1, 2, 3, 4, and consequently to objective 5, as well as to objective 7, as mentioned in previous sections. These contributions represented the core of the team's research activity over the evaluation period, as stressed by our publications. It is however noticeable that multi-scale modeling of the immune response and of pathological hematopoiesis (leukemia) has come to represent a proportionally more important part of our activity.

Objective 6 has been pursued, the project chronos evolved to a better defined project SiMuScale that is currently being developed and aims at structuring the team's activity and providing a simulation platform that could be adapted to various biological questions necessitating multi-scale modeling.

Objectives for the next four years

The main objectives for the next four years are to continue to improve the 3 previous points: 1) Mathematical and computational modeling for cell population dynamics; 2) Multi-scale modeling of hematopoiesis and leukemia; 3) Multi-scale modeling of the immune response. In addition, we will pursue our effort to develop a simulation platform for multi-scale models (SiMuScale) and we intend to develop the use of mixed effect models and other statistical approaches to deal with the challenges offered by modern biology, in particular the generation of single cell data.

5.1.1 Reverse engineering of a mechanistic model of gene expression using metastability and temporal dynamics

Differentiation can be modeled at the single cell level as a stochastic process resulting from the dynamical functioning of an underlying Gene Regulatory Network (GRN), driving stem or progenitor cells to one or many differentiated cell types. Metastability seems inherent to differentiation process as a consequence of the limited number of cell types. Moreover, mRNA is known to be generally produced by bursts, which can give rise to highly variable non-Gaussian behavior, making the estimation of a GRN from transcriptional profiles challenging. In the paper 26 (see also the thesis 29), we present CARDAMOM (Cell type Analysis from scRna-seq Data achieved from a Mixture MOdel), a new algorithm for inferring a GRN from timestamped scRNA-seq data, which crucially exploits these notions of metastability and transcriptional bursting. We show that such inference can be seen as the successive resolution of as many regression problem as timepoints, after a preliminary clustering of the whole set of cells with regards to their associated bursts frequency. We demonstrate the ability of CARDAMOM to infer a reliable GRN from in silico expression datasets, with good computational speed. To the best of our knowledge, this is the first description of a method which uses the concept of metastability for performing GRN inference.

5.1.2 The best of both worlds: Combining population genetic and quantitative genetic models

Numerous traits under migration-selection balance are shown to exhibit complex patterns of genetic architecture with large variance in effect sizes. However, the conditions under which such genetic architectures are stable have yet to be investigated, because studying the influence of a large number of small allelic effects on the maintenance of spatial polymorphism is mathematically challenging, due to the high complexity of the systems that arise. In particular, in the most simple case of a haploid population in a two-patch environment, while it is known from population genetics that polymorphism at a single major-effect locus is stable in the symmetric case, there exists no analytical predictions on how this polymorphism holds when a polygenic background also contributes to the trait. In 14 (see also the thesis 27), we propose to answer this question by introducing a new eco-evo methodology that allows us to take into account the combined contributions of a major-effect locus and of a quantitative background resulting from small-effect loci, where inheritance is encoded according to an extension to the infinitesimal model. In a regime of small variance contributed by the quantitative loci, we justify that traits are concentrated around the major alleles, according to a normal distribution, using new convex analysis arguments. This allows a reduction in the complexity of the system using a separation of time scales approach. We predict an undocumented phenomenon of loss of polymorphism at the major-effect locus despite strong selection for local adaptation, because the quantitative background slowly disrupts the rapidly established polymorphism at the major-effect locus, which is confirmed by individual-based simulations. Our study highlights how segregation of a quantitative background can greatly impact the dynamics of major-effect loci by provoking migrational meltdowns. We also provide a comprehensive toolbox designed to describe how to apply our method to more complex population genetic models.

5.1.3 Hematopoietic differentiation is characterized by a transient peak of entropy at a single-cell level

Background: Mature blood cells arise from hematopoietic stem cells in the bone marrow by a process of differentiation along one of several different lineage trajectories. This is often represented as a series of discrete steps of increasing progenitor cell commitment to a given lineage, but as for differentiation in general, whether the process is instructive or stochastic remains controversial. In 15, we examine this question by analyzing single-cell transcriptomic data from human bone marrow cells, assessing cell-to-cell variability along the trajectories of hematopoietic differentiation into four different types of mature blood cells. The instructive model predicts that cells will be following the same sequence of instructions and that there will be minimal variability of gene expression between them throughout the process, while the stochastic model predicts a role for cell-to-cell variability when lineage commitments are being made. Results: Applying Shannon entropy to measure cell-to-cell variability among human hematopoietic bone marrow cells at the same stage of differentiation, we observed a transient peak of gene expression variability occurring at characteristic points in all hematopoietic differentiation pathways. Strikingly, the genes whose cell-to-cell variation of expression fluctuated the most over the course of a given differentiation trajectory are pathway-specific genes, whereas genes which showed the greatest variation of mean expression are common to all pathways. Finally, we showed that the level of cell-to-cell variation is increased in the most immature compartment of hematopoiesis in myelodysplastic syndromes. Conclusions: These data suggest that human hematopoietic differentiation could be better conceptualized as a dynamical stochastic process with a transient stage of cellular indetermination, and strongly support the stochastic view of differentiation. They also highlight the need to consider the role of stochastic gene expression in complex physiological processes and pathologies such as cancers, paving the way for possible noise-based therapies through epigenetic regulation.

5.1.4 CD8 memory precursor cell generation is a continuous process

In the paper 25, we studied the generation of memory precursor cells following an acute infection by analyzing single-cell RNA-seq data that contained CD8 T cells collected during the postinfection expansion phase. We used different tools to reconstruct the developmental trajectory that CD8 T cells followed after activation. Cells that exhibited a memory precursor signature were identified and positioned on this trajectory. We found that these memory precursors are generated continuously with increasing numbers arising over time. Similarly, expression of genes associated with effector functions was also found to be raised in memory precursors at later time points. The ability of cells to enter quiescence and differentiate into memory cells was confirmed by BrdU pulse-chase experiment in vivo. Analysis of cell counts indicates that the vast majority of memory cells are generated at later time points from cells that have extensively divided.

5.1.5 Theoretical evidence of osteoblast self-inhibition after activation of the genetic regulatory network controlling mineralization

Bone is a hard-soft biomaterial built through a self-assembly process under genetic regulatory network (GRN) monitoring. The paper 12 aims to capture the behavior of the bone GRN part that controls mineralization by using a mathematical model. Here, we provide an advanced review of empirical evidence about interactions between gene coding (i) transcription factors and (ii) bone proteins. These interactions are modeled with nonlinear differential equations using Michaelis-Menten and Hill functions. Compared to empirical evidence - coming from osteoblasts culture -, the two best systems use factors of inhibition from the start of the activation of each gene. It reveals negative indirect interactions coming from either negative feedback loops or the recently depicted micro-RNAs. The difference between the two systems also lies in the BSP equation and two ways for activating and reducing its production. Thus, it highlights the critical role of BSP in the bone GRN that acts on bone mineralization. Our study provides the first theoretical evidence of osteoblast self-inhibition after activation of the genetic regulatory network controlling mineralization with this work.

5.2.1 Infection spreading in cell culture as a reaction-diffusion wave

Infection spreading in cell culture occurs due to virus replication in infected cells and its random motion in the extracellular space. Multiplicity of infection experiments in cell cultures are conventionally used for the characterization of viral infection by the number of viral plaques and the rate of their growth. In 7, we describe this process with a delay reaction-diffusion system of equations for the concentrations of uninfected cells, infected cells, virus, and interferon. Time delay corresponds to the duration of viral replication inside infected cells. We show that infection propagates in cell culture as a reaction-diffusion wave, we determine the wave speed and prove its existence. Next, we carry out numerical simulations and identify three stages of infection progression: infection decay during time delay due to virus replication, explosive growth of viral load when infected cells begin to reproduce it, and finally, wave-like infection progression in cell culture characterized by a constant or slowly growing total viral load. The modelling results are in agreement with the experimental data for the coronavirus infection in a culture of epithelial cells and for some other experiments. The presence of interferon produced by infected cells decreases the viral load but does not change the speed of infection progression in cell culture. In the 2D modelling, the total viral load grows faster than in the 1D case due to the increase of plaque perimeter.

5.2.2 Viral infection spreading and mutation in cell culture

A new model of viral infection spreading in cell cultures is proposed in the paper 8, taking into account virus mutation. This model represents a reaction-diffusion system of equations with time delay for the concentrations of uninfected cells, infected cells and viral load. Infection progression is characterized by the virus replication number Rv, which determines the total viral load. Analytical formulas for the speed of propagation and for the viral load are obtained and confirmed by numerical simulations. It is shown that virus mutation leads to the emergence of a new virus variant. Conditions of the coexistence of the two variants or competitive exclusion of one of them are found, and different stages of infection progression are identified.

5.2.3 Virus replication and competition in a cell culture: Application to the SARS-CoV-2 variants

Viral replication in a cell culture is described in the paper 9 by a delay reaction-diffusion system. It is shown that infection spreads in cell culture as a reaction-diffusion wave, for which the speed of propagation and viral load can be determined both analytically and numerically. Competition of two virus variants in the same cell culture is studied, and it is shown that the variant with larger individual wave speed outcompetes another one, and eliminates it. This approach is applied to the Delta and Omicron variants of the SARS-CoV-2 infection in the cultures of human epithelial and lung cells, allowing characterization of infectivity and virulence of each variant, and their comparison.

5.3.1 The effect of lenvatinib and pembrolizumab on thyroid cancer refractory to iodine 131I simulated by mathematical modeling

Immunotherapy and targeted therapy are alternative treatments to differentiated thyroid cancer (DTC), which is usually treated with surgery and radioactive iodine. However, in advanced thyroid carcinomas, molecular alterations can cause a progressive loss of iodine sensitivity, thereby making cancer resistant to radioactive iodine-refractory (RAIR). In the treatment of cancer, tyrosine kinase inhibitors are administered to prevent the growth of cancer cells. One such inhibitor, lenvatinib, forms a targeted therapy for RAIR-DTC, while the immunotherapeutic pembrolizumab, a humanized antibody, prevents the binding of programmed cell death ligand 1 (PD-L1) to the PD-1 receptor. As one of the first studies on treatments for thyroid cancer with mathematical model involving immunotherapy and targeted therapy, we developed in the paper 20, an ordinary differential system and tested variables such as concentration of lenvatinib and pembrolizumab, total cancer cells, and number of immune cells (i.e., T cells and natural killer cells). Analyzing local and global stability and the simulated action of drugs in patients with RAIR-DTC, revealed the combined effect of the targeted therapy with pembrolizumab. The scenarios obtained favor the combined therapy as the best treatment option, given its unrivaled ability to boost the immune system’s rate of eliminating tumor cells.

5.3.2 Discrete maturity and delay differential-difference model of hematopoietic cell dynamics with applications to Acute Myenogenous Leukemia

In the last few years, many efforts were oriented towards describing the hematopoiesis phenomenon in normal and pathological situations. This complex biological process is organized as a hierarchical system that begins with primitive hematopoietic stem cells (HSCs) and ends with mature blood cells: red blood cells, white blood cells and platelets. Regarding acute myelogenous leukemia (AML), a cancer of the bone marrow and blood, characterized by a rapid proliferation of immature cells, which eventually invade the bloodstream, there is a consensus about the target cells during the HSCs development which are susceptible to leukemic transformation. We propose and analyze in 2 a mathematical model of HSC dynamics taking into account two phases in the cell cycle, a resting and a proliferating one, by allowing just after division a part of HSCs to enter the resting phase and the other part to come back to the proliferating phase to divide again. The resulting mathematical model is a system of nonlinear differential-difference equations. Due to the hierarchical organization of the hematopoiesis, we consider n stages of HSCs characterized by their maturity levels. We obtain a system of 2n nonlinear differential-difference equations. We study the existence, uniqueness, positivity, boundedness and unboundedness of the solutions. We then investigate the existence of positive and axial steady states for the system, and obtain conditions for their stability. Sufficient conditions for the global asymptotic stability of the trivial steady state as well as conditions for its instability are obtained. Using neutral differential equation associated to the differential-difference system, we also obtain results on the local asymptotic stability of the positive steady state. Numerical simulations are carried out to show the influence of variations of the differentiation rates and self-renewal coefficients of the HSCs on the behavior of the system. In particular, we show that a blocking of differentiation at an early stage of HSC development can lead in an overexpression of very immature cells. Such situation corresponds to the observation in the case of AML.

5.4.1 Traveling waves for reaction-diffusion PDE coupled to difference equation with nonlocal dispersal term and time delay

We consider in 3 a class of biological models represented by a system composed of reaction diffusion PDE coupled with difference equations (renewal equations) in n -dimensional space, with nonlocal dispersal terms and implicit time delays. The difference equation generally arises, by means of the method of characteristics, from an age-structured partial differential system. Using upper and lower solutions, we study the existence of monotonic planar traveling wave fronts connecting the extinction state to the uniform positive state. The corresponding minimum wave speed is also obtained. In addition, we investigate the effect of the parameters on this minimum wave speed and we give a detailed analysis of its asymptotic behavior.

5.4.2 Non-local competition slows down front acceleration during dispersal evolution

We investigate in 10 the super-linear spreading in a reaction-diffusion model analogous to the Fisher-KPP equation, but in which the population is heterogeneous with respect to the dispersal ability of individuals, and the saturation factor is non-local with respect to one variable. We prove that the rate of acceleration is slower than the rate of acceleration predicted by the linear problem, that is, without saturation. This hindering phenomenon is the consequence of a subtle interplay between the non-local saturation and the non-trivial dynamics of some particular curves that carry the mass at the front. A careful analysis of these trajectories allows us to identify the value of the rate of acceleration. The article is complemented with numerical simulations that illustrate some behavior of the model that is beyond our analysis.

5.4.3 Dynamics of lineages in adaptation to a gradual environmental change

We investigate in 11 a simple quantitative genetics model subjet to a gradual environmental change from the viewpoint of the phylogenies of the living individuals. We aim to understand better how the past traits of their ancestors are shaped by the adaptation to the varying environment. The individuals are characterized by a one-dimensional trait. The dynamics-births and deaths-depend on a time-changing mortality rate that shifts the optimal trait to the right at constant speed. The population size is regulated by a nonlinear non-local logistic competition term. The macroscopic behaviour can be described by a PDE that admits a unique positive stationary solution. In the stationary regime, the population can persist, but with a lag in the trait distribution due to the environmental change. For the microscopic (individual-based) stochastic process, the evolution of the lineages can be traced back using the historical process, that is, a measure-valued process on the set of continuous real functions of time. Assuming stationarity of the trait distribution, we describe the limiting distribution, in large populations, of the path of an individual drawn at random at a given time T. Freezing the non-linearity due to competition allows the use of a many-to-one identity together with Feynman-Kac's formula. This path, in reversed time, remains close to a simple Ornstein-Uhlenbeck process. It shows how the lagged bulk of the present population stems from ancestors once optimal in trait but still in the tail of the trait distribution in which they lived.

5.4.4 Evolutionary dynamics of complex traits in sexual populations in a heterogeneous environment: how normal?

When studying the dynamics of trait distribution of populations in a heterogeneous environment, classical models from quantitative genetics choose to look at its system of moments, specifically the first two ones. Additionally, in order to close the resulting system of equations, they often assume that the trait distribution is Gaussian (see for instance Ronce and Kirkpatrick 2001). The aim of the paper 13 is to introduce a mathematical framework that follows the whole trait distribution (without prior assumption) to study evolutionary dynamics of sexually reproducing populations. Specifically, it focuses on complex traits, whose inheritance can be encoded by the infinitesimal model of segregation (Fisher 1919). We show that it allows us to derive a regime in which our model gives the same dynamics as when assuming a Gaussian trait distribution. To support that, we compare the stationary problems of the system of moments derived from our model with the one given in Ronce and Kirkpatrick 2001 and show that they are equivalent under this regime and do not need to be otherwise. Moreover, under this regime of equivalence, we show that a separation bewteen ecological and evolutionary time scales arises. A fast relaxation toward monomorphism allows us to reduce the complexity of the system of moments, using a slow-fast analysis. This reduction leads us to complete, still in this regime, the analytical description of the bistable asymmetrical equilibria numerically found in Ronce and Kirkpatrick 2001. More globally, we provide explicit modelling hypotheses that allow for such local adaptation patterns to occur.

5.4.5 Analysis of a model of cell crawling migration

We introduce and study in 24 a model for motility of cells on substrate. The cell is 1d, inextensible and it contains a diffusive back-polarity marker, which satisfies a non-linear and non-local parabolic equation of Fokker-Planck type with attachment/detachment at the boundary. The idea behind the model is a quadratic nonlinear coupling: the marker is advected by the cell velocity, which is itself driven by a front-rear imbalance in marker. We show that it is of bistable type, provided that the coupling between the asymmetry of the marker and the cell velocity is sufficiently strong. In such a case we prove the non-linear stability of the largest steady state, for large initial data. In the weak coupling case we prove the convergence of the molecular concentration towards the Gaussian state.

5.5.1 Immuno-epidemiological model-based prediction of further Covid-19 epidemic outbreaks due to immunity waning

In 17, we develop a new data-driven immuno-epidemiological model with distributed infectivity, recovery and death rates determined from the epidemiological, clinical and experimental data. Immunity in the population is taken into account through the time-dependent number of vaccinated people with different numbers of doses and through the acquired immunity for recovered individuals. The model is validated with the available data. We show that for the first time from the beginning of pandemic COVID-19 some countries reached collective immunity. However, the epidemic continues because of the emergence of new variant BA.2 with a larger immunity escape or disease transmission rate than the previous BA.1 variant. Large epidemic outbreaks can be expected several months later due to immunity waning. These outbreaks can be restrained by an intensive booster vaccination.

5.5.2 An epidemic model with time delay determined by the disease duration

Immuno-epidemiological models with distributed recovery and death rates can describe the epidemic progression more precisely than conventional compartmental models. However, the required immunological data to estimate the distributed recovery and death rates are not easily available. In 18, an epidemic model with time delay is derived from the previously developed model with distributed recovery and death rates, which does not require precise immunological data. The resulting generic model describes epidemic progression using two parameters, disease transmission rate and disease duration. The disease duration is incorporated as a delay parameter. Various epidemic characteristics of the delay model, namely the basic reproduction number, the maximal number of infected, and the final size of the epidemic are derived. The estimation of disease duration is studied with the help of real data for COVID-19. The delay model gives a good approximation of the COVID-19 data and of the more detailed model with distributed parameters.

5.5.3 An epidemic model with time-distributed recovery and death rates

A compartmental epidemiological model with distributed recovery and death rates is proposed in 19. In some particular cases, the model can be reduced to the conventional SIR model. However, in general, the dynamics of epidemic progression in this model is different. Distributed recovery and death rates are evaluated from COVID-19 data. The model is validated by the epidemiological data for different countries, and it shows better agreement with the data than the SIR model. The time-dependent disease transmission rate is estimated.

5.5.4 Stability analysis of a delayed immune response model to viral infection

The purpose of the work 16 is the study of the qualitative behavior of the homogeneous in space solution of a delay differential equation arising from a model of infection dynamics. This study is mainly based on the monotone dynamical systems theory. Existence and smoothness of solutions are proved, and conditions of asymptotic stability of equilibriums in the sense of monotone dynamical systems are formulated. Then, sufficient conditions of global stability of the nonzero steady state are derived, for the two typical forms of the function f, specifying the efficiency of immune response-mediated virus elimination. Numerical simulations illustrate the analytical results. The obtained theoretical results have been applied, in a context of COVID-19 data calibration, to forecast the immunological behaviour of a real patient.

5.5.5 Global asymptotic stability for a distributed delay differential-difference system of a Kermack-McKendrick SIR model

We investigate in 4 a system of distributed delay differential-difference equations describing an epidemic model of susceptible, infected, recovered and temporary protected population dynamics. A nonlocal term (distributed delay) appears in this model to describe the temporary protection period of the susceptible individuals. We investigate mathematical properties of the model. We obtain the global asymptotic stability of the two steady states: disease-free and endemic. We construct appropriate Lyapunov functionals where the basic reproduction number appears as a threshold for the global asymptotic behavior of the solution between disease extinction and persistence.

5.5.6 Traveling waves of a differential-difference diffusive Kermack-McKendrick epidemic model with age-structured protection phase

We consider in 5 a general class of diffusive Kermack-McKendrick SIR epidemic models with an age-structured protection phase with limited duration, for example due to vaccination or drugs with temporary immunity. A saturated incidence rate is also considered which is more realistic than the bilinear rate. The characteristics method reduces the model to a coupled system of a reaction-diffusion equation and a continuous difference equation with a time-delay and a nonlocal spatial term caused by individuals moving during their protection phase. We study the existence and non-existence of non-trivial traveling wave solutions. We get almost complete information on the threshold and the minimal wave speed that describes the transition between the existence and non-existence of non-trivial traveling waves that indicate whether the epidemic can spread or not. We discuss how model parameters, such as protection rates, affect the minimal wave speed. The difficulty of our model is to combine a reaction-diffusion system with a continuous difference equation. We deal with our problem mainly by using Schauder's fixed point theorem. More precisely, we reduce the problem of the existence of non-trivial traveling wave solutions to the existence of an admissible pair of upper and lower solutions.

5.5.7 Forecasting the effect of Pre-Exposure Prophylaxis (PrEP) on HIV propagation with a system of differential–difference equations with delay

The HIV/AIDS epidemic is still active worldwide with no existing definitive cure. Based on the WHO recommendations stated in 2014, a treatment, called Pre-Exposure Prophylaxis (PrEP), has been used in the world, and more particularly in France since 2016, to prevent HIV infections. In the paper 6, we propose a new compartmental epidemiological model with a limited protection time offered by this new treatment. We describe the PrEP compartment with an age-structure hyperbolic equation and introduce a differential equation on the parameter that governs the PrEP starting process. This leads us to a nonlinear differential–difference system with discrete delay. After a local stability analysis, we prove the global behavior of the system. Finally, we illustrate the solutions with numerical simulations based on the data of the French Men who have Sex with Men (MSM) population. We show that the choice of a logistic time dynamics combined with our Hill-function-like model leads to a perfect data fit. These results enable us to forecast the evolution of the HIV epidemics in France if the populations keep using PrEP.

7.1.1 Inria associate team not involved in an IIL or an international program

•  Associated team MathModelingHematopoiesis “Mathematical modeling of hematopoietic stem cell dynamics in normal and pathological hematopoiesis with optimal control for drug therapy”, 2019 - 2022 (stopped in 2020 due to COVID-19).
  •  Participants (Dracula): M. Adimy [Coordinator], L. Pujo-Menjouet and V. Volpert.
  •  Partner Institution(s) from India: Presidency University, Kolkata - Mathematics Department of Indian Institute of Technology, Roorkee - Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur.
  •  The project proposes to develop and analyse new mathematical models of Hematopoietic Stem Cell population dynamics in normal and pathological hematopoiesis. Two important questions will be explored in this project: i) the biological data concerning the hematopoiesis process evolves constantly, and new understanding modifies the established mathematical models, ii) modeling constraints us to simplify the complicated biological scenarios, which moving away from the reality, but enabling us to reach a certain comprehension of the hematopoiesis process.
•  Associated team MoCoVec “Modelling and Biological Control of Vector-Borne Diseases: the case of Malaria and Dengue”, 2022-2025.
  •  Participants (Dracula): M. Adimy.
  •  Partner Institution(s): MAMBA Inria, Paris (P.A. Bliman [Coordinator]) - FAPESP São Paulo, Brazil.
  •  Focusing on dengue and malaria, two diseases transmitted by vector mosquito and which cause high morbidity and mortality around the world, this project aims to model disease transmission, its spread and control, in a context of climatic and environmental change. For this, the main drives of disease transmission will be addressed to understand which factors modulate the spatio-temporal patterns observed, especially in Brazil.

7.1.2 STIC/MATH/CLIMAT AmSud projects

•  STIC AmSud project NEMBICA “New methods for biological control of the arboviruses”, 2019-2022.
  •  Participants (Dracula): M. Adimy.
  •  Partner Institution(s): MAMBA Inria, Paris (P.A. Bliman [Coordinator]) - CIRAD - CNRS - Argentina - Chile - Colombia - Paraguay.
  •  This project is concerned with new strategies of biological control of the spread of many and important diseases transmitted by mosquitoes of the genus Aedes, which put at risk considerable portions of the human population and infect millions of people every year. The aim is to elaborate and analyze pertinent models, and to evaluate qualitatively and quantitatively different control strategies, with the goal of understanding the key aspects and parameters of the dynamics, testing concepts, estimating feasibility, identifying risks and reducing cost.
•  MATH AmSud project TOMENADE “Topological methods and non autonomous dynamics for delay differential equations”, 2022-2024.
  •  Participants (Dracula): M. Adimy.
  •  Partner Institution(s): Laboratoire des Signaux et Systèmes (L2S), CNRS, Centrale Supelec - Argentina (P. Amster [Coordinator]) - Chile - Brazil.
  •  This project addresses open problems about non autonomous systems of delay differential equations modeling some phenomena from life sciences, namely, a meta-populations version of the Nicholson equations and models of competition in a stirred chemostat. Nevertheless, the ideas and methods could be certainly extended in several ways, and we also expect to make progress in topics as the (non autonomous) topological linearization problem and the possibility of converse results for persistence.

7.1.3 Participation in other International Programs

•  ECOS-Sud France-Chilie, C20E03 “Coarsening dynamics: numerical and theoretical analysis of the Lifchitz-Slyozov equation with nucleation and applications to biology”, 2021-2023.
  •  Participants (Dracula): L. Pujo-Menjouet and L. Tine.
  •  Partner Institution(s): Inria ANACONDA - Institut Denis Poisson, University Orléans - Universidad del Bio-Bio, Concepcion, Chilie (E. Hingant, [Coordinator]).
  •  The general objectives of this project are i) To push-forward theoretical studies on well-posedness of solutions of the Lifshitz- Slyozov model and variants, and understand long-time behavior and scaling properties of those solutions, ii) To explore various numerical strategies to accurately simulate solutionsoft heLifshitz-Slyozov model, iii) To apply our developed methodology on biology applications, in particular within interdisciplinary work on protein aggregation in neurodegenerative diseases, and on adipocyte formation dynamics.
•  IFCAM1 funds “Mathematical modeling of hematopoiesis process in application to chronic and acute myelogenous leukemia”, 2018-2021 (stopped in 2020 due to COVID-19).
  •  Participants (Dracula): M. Adimy [Coordinator], L. Pujo-Menjouet and V. Volpert.
  •  Partner Institution(s) from India: Presidency University, Kolkata - Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur.
  •  The project proposes to develop and analyze new realistic mathematical models of blood cells formation in the bone marrow (hematopoiesis). Two important scientific questions will be explored in this project: i) the biological data concerning the hematopoiesis process evolves constantly, and new understanding modifies the established mathematical models, ii) modeling constraints us to simplify the complicated biological scenarios, which moving away from the reality, but enabling us to reach a certain comprehension of the hematopoiesis process. The challenging task is to combine biological, mathematical and numerical approaches to obtain better perceiving of the underlying mechanisms between normal and pathological hematopoiesis. Thus, we shall investigate different mathematical models, mainly based on age-structured and delay differential equations, to shed new light on the understanding of specific biological phenomena observed during pathological hematopoiesis (for instance, the appearance of oscillations in patients with Chronic Myeloid Leukemia (CML); Or, the overproduction of blasts in patients with Acute Myeloid Leukemia (AML)).
•  PHC-Maghreb “Mathematical modeling and control of the spread of infectious diseases in the Mediterranean area”, 2022-2024.
  •  Participants (Dracula): Samuel Bernard, Vitaly Volpert, Léon Matar Tine [Coordinator].
  •  Partner Institution(s): Inria-Dracula, ICJ (Université Lyon 1), Mohammed V University of Rabat, Ecole Nationale d'Ingénieurs de Tunis, Université Tlemcen
  •  This research project aims to contribute to the development of some decision-making tools in the context of major global public health challenges: namely the modelling, monitoring and control of the spread of infectious diseases in the socio-economic current context. To do this, it is a question of contributing to: 1) improving mathematical representations of the human immune system, 2) construction of compartmental epidemiological models in which susceptible individuals are divided into several classes according to their immunity (vaccinated or not, age, infection with or without provisional immunity, infection with or without recurrence, etc.).
•  Mecan'os “Si tu ne peux pas l’avoir, (re)construis le !” 2021-2023
  •  Participants (Dracula): L. Pujo-Menjouet [Coordinator].
  •  Partner Institution(s): Institut Camille Jordan - CUNY, New-York - University of Tlemcen, Algeria.
  •  The aim of this project is to describe the gene regulatory network involving osteoblasts and its interactions with key proteins in the mineralization of the collagen matrix. A feedback loop from the matrix stiffness induces whole control of the proteins. The question is how. The application is to be able to produce bio-materials showing any required stiffness properties for bone substitutes for instance.
•  micrOS-macrOS “Modélisation multi-échelle de l'os”, 2021-2023
  •  Participants (Dracula): L. Pujo-Menjouet [Coordinator].
  •  Partner Institution(s): Institut Camille Jordan - CUNY, New-York - University of Tlemcen, Algeria.
  •  The objective of this project is to understand the impact of the gene regulatory network (at the molecular scale) on the bio-mechanic properties of the bone (bone scale). This new multi-scale approach will allow to finely understand the qualitative and quantitative role of osteoblasts and osteoclasts on the normal or pathological bone formation.

7.2.1 H2020 projects

7.3.1 ANR

7.3.2 Other projects

8.1.1 Scientific events: organisation

8.1.2 Journal

8.2.1 Supervision

• PhD of Kyriaki Dariva, "Contributions à l'étude de la stabilité dans des modèles de populations de cellules". University Lyon 1, until June 20, 2022, supervisor: Thomas Lepoutre.
• PhD of Léonard Dekens, "Adaptation d'une population avec une reproduction sexuée à un environnement hétérogène : modélisation mathématique et analyse asymptotique dans un régime de petite variance", University Lyon 1, until July 07, 2022, supervisor: Vincent Calvez.
• PhD of Mete Demircigil, "Etude du mouvement collectif chez Dictyostelium discoideum et autres espèces. Modélisation, Analyse et Simulation", ENS-Lyon, until August 26, 2022, supervisor: Vincent Calvez.
• PhD of Elias Ventre, "Analyse, calibration et évaluation de modèles stochastiques d'expression des gènes", ENS-Lyon, until September 28, 2022, supervisors: Olivier Gandrillons, Thibault Espinasse and Thomas Lepoutre.
• PhD in progress: Cheikh Gueye, "Problèmes inverses pour l'estimation de paramètres de modèles mathématiques: Application en dynamique des populations", University Lyon 1 and University Cheikh Anta Diop of Dakar, since October 16, 2018, supervisors: Ionel-sorinel Ciuperca, Abdoulaye Sene and de Léon matar Tine.
• PhD in progress: Matteo Bouvier, "Identification et contrôle de réseaux de régulation de gènes", CIFRE with the Vidium company and ENS-Lyon, since October 01, 2020, supervisor: Olivier Gandrillon.
• PhD in progress: Margaux Prieux, "Etude des réseaux de régulation de la différenciation des CD8 mémoire par une approche moléculaire au niveau cellule unique", ENS-Lyon, since October 01, 2019, supervisors: Olivier Gandrillon and Jacqueline Marvel.
• PhD in progress: Grégoire Ranson, "Mathematical modeling of epidemics spreading dealing with temporary treatment effciency", University Lyon 1 and York University, since April 27, 2022, supervisors: Mostafa Adimy, Laurent Pujo-Menjoeut and Jianhong Wu.
• PhD in Progress: Charlotte Dugourd, "Nested Immuno-epidemiological modeling of the dynamics of intra- and inter-host infections", Université Lyon 1, since October 01, 2022, supervisor: Mostafa Adimy.
• PhD in progress: Arsène Marzorati, University Lyon 1, since October 01, 2022, supervisors: Samuel Bernard and Jonathan Rouzaud-Cornabas.
• PhD in progress: Basile Fornara, "Mécanismes de dissémination des prions dans les tissus cérébraux : une approche synthétique",Université Paris Cité, since October 21, 2022, supervisors: Human Rezaei et de Laurent Pujo-menjouet.
• PhD in progress: Maxime Estavoyer, "Modélisation mathématique de la formation des plumes d'oiseaux: interaction entre propagation instruction et auto-organisation", University Lyon 1, since March 03, 2022, supervisor: Thomas Lepoutre.
• Post-doc: Thao Nguyen Thi Nhu, since February 2022, supervisors: Olivier Gandrillon.
• Post-doc: Nicolas Torres, since April 2022, supervisors: Laurent Pujo-Menjouet.
• Post-doc: Michèle Romanos, since December 2022, supervisors: Vincent Calvez.

International journals

• 1 articleM.Mostafa Adimy, L.Louis Babin and L.Laurent Pujo-Menjouet. Why Are Periodic Erythrocytic Diseases so Rare in Humans?Bulletin of Mathematical Biology8419January 2022, 1-19
  HALDOIback to text
• 2 articleM.Mostafa Adimy, A.Abdennasser Chekroun, A.Abderrahim El Abdllaoui and A.Arsène Marzorati. DISCRETE MATURITY AND DELAY DIFFERENTIAL-DIFFERENCE MODEL OF HEMATOPOIETIC CELL DYNAMICS WITH APPLICATIONS TO ACUTE MYELOGENOUS LEUKEMIA.Journal of Biological Systems3003September 2022, 497-527
  HALDOIback to text
• 3 articleM.Mostafa Adimy, A.Abdennasser Chekroun and B.Bogdan Kazmierczak. Traveling waves for reaction-diffusion PDE coupled to difference equation with nonlocal dispersal term and time delay.Mathematical Modelling of Natural Phenomena172022, 17
  HALDOIback to text
• 4 articleM.Mostafa Adimy, A.Abdennasser Chekroun and T.Toshikazu Kuniya. Global asymptotic stability for a distributed delay differential-difference system of a Kermack-McKendrick SIR model.Applicable AnalysisMay 2022, 1-13
  HALDOIback to text
• 5 articleM.Mostafa Adimy, A.Abdennasser Chekroun and T.Toshikazu Kuniya. Traveling waves of a differential-difference diffusive Kermack-McKendrick epidemic model with age-structured protection phase.Journal of Mathematical Analysis and Applications5051January 2022, 125464
  HALDOIback to text
• 6 articleM.Mostafa Adimy, J.Julien Molina, L.Laurent Pujo-Menjouet, G.Grégoire Ranson and J.Jianhong Wu. Forecasting the Effect of Pre-Exposure Prophylaxis (PrEP) on HIV Propagation with a System of Differential–Difference Equations with Delay.Mathematics 1021November 2022, 4093
  HALDOIback to text
• 7 articleL.Latifa Ait Mahiout, N.Nikolai Bessonov, B.Bogdan Kazmierczak, G.Georges Sadaka and V.Vitaly Volpert. Infection spreading in cell culture as a reaction-diffusion wave.ESAIM: Mathematical Modelling and Numerical Analysis563May 2022, 791-814
  HALDOIback to text
• 8 articleL.Latifa Ait Mahiout, B.Bogdan Kazmierczak and V.Vitaly Volpert. Viral Infection Spreading and Mutation in Cell Culture.Mathematics 10January 2022
  HALDOIback to text
• 9 articleL.L Ait Mahiout, A.Anastasia Mozokhina, A.A Tokarev and V.V Volpert. Virus replication and competition in a cell culture: Application to the SARS-CoV-2 variants.Applied Mathematics Letters133May 2022
  HALDOIback to text
• 10 articleV.Vincent Calvez, C.Christopher Henderson, S.Sepideh Mirrahimi, O.Olga Turanova and T.Thierry Dumont. Non-local competition slows down front acceleration during dispersal evolution.Annales Henri Lebesgue2022
  HALback to text
• 11 articleV.Vincent Calvez, B.Benoît Henry, S.Sylvie Méléard and V. C.Viet Chi Tran. Dynamics of lineages in adaptation to a gradual environmental change.Annales Henri Lebesgue5July 2022, 729-777
  HALDOIback to text
• 12 articleA.Abdennasser Chekroun, L.Laurent Pujo-Menjouet, S.Steve Falcoz, K.Kamyine Tsuen, K.Kevin Yueh-Hsun Yang and J.-P.Jean-Philippe Berteau. Theoretical evidence of osteoblast self-inhibition after activation of the genetic regulatory network controlling mineralization.Journal of Theoretical Biology537March 2022, 111005
  HALDOIback to text
• 13 article L.Léonard Dekens. Evolutionary dynamics of complex traits in sexual populations in a heterogeneous environment: how normal? Journal of Mathematical Biology February 2022
  HAL back to text
• 14 articleL.L Dekens, S. P.S P Otto and V.V Calvez. The best of both worlds: Combining population genetic and quantitative genetic models.Theoretical Population Biology148December 2022, 49-75
  HALDOIback to text
• 15 articleC.Charles Dussiau, A.Agathe Boussaroque, M.Mathilde Gaillard, C.Clotilde Bravetti, L.Laila Zaroili, C.Camille Knosp, C.Chloé Friedrich, P.Philippe Asquier, L.Lise Willems, L.Laurent Quint, D.Didier Bouscary, M.Michaela Fontenay, T.Thibault Espinasse, A.Adriana Plesa, P.Pierre Sujobert, O.Olivier Gandrillon and O.Olivier Kosmider. Hematopoietic differentiation is characterized by a transient peak of entropy at a single-cell level.BMC Biology201March 2022, 60
  HALDOIback to text
• 16 articleJ.Jaafar El Karkri, F.Fatima Boudchich, V.Vitaly Volpert and R.Rajae Aboulaich. Stability Analysis of a Delayed Immune Response Model to Viral Infection.Differential Equations and Dynamical SystemsJanuary 2022
  HALDOIback to text
• 17 articleS.Samiran Ghosh, M.Malay Banerjee and V.Vitaly Volpert. Immuno-Epidemiological Model-Based Prediction of Further Covid-19 Epidemic Outbreaks Due to Immunity Waning.Mathematical Modelling of Natural Phenomena172022
  HALDOIback to text
• 18 articleS.Samiran Ghosh, V.Vitaly Volpert and M.Malay Banerjee. An Epidemic Model with Time Delay Determined by the Disease Duration.Mathematics 10July 2022
  HALDOIback to text
• 19 articleS.Samiran Ghosh, V.Vitaly Volpert and M.Malay Banerjee. An Epidemic Model with Time-Distributed Recovery and Death Rates.Bulletin of Mathematical Biology84June 2022
  HALDOIback to text
• 20 articleJ.Jairo Gomes Da Silva, I. C.Izabel Cristina Rodrigues Da Silva, M.Mostafa Adimy and P. F.Paulo Fernando de Arruda Mancera. The effect of lenvatinib and pembrolizumab on thyroid cancer refractory to iodine 131I simulated by mathematical modeling.Journal of Biological Systems3001March 2022, 93-112
  HALDOIback to text
• 21 articleM.Maxim Kuznetsov, J.Jean Clairambault and V.Vitali Volpert. Perspectives in cancer treatment. Reply to comments on "Improving cancer treatments via dynamical biophysical models".Physics of Life ReviewsMay 2022
  HAL
• 22 articleC.Cristina Leon, I.Irina Kutsenko and V.Vitaly Volpert. Existence of solutions for a nonlocal reaction-diffusion equation in biomedical applications.Israel Journal of Mathematics248March 2022, 67 - 93
  HALDOI
• 23 articleC.Cristina Leon, A. A.Alexey A Tokarev and V. A.Vitaly A Volpert. Modelling of cytokine storm in respiratory viral infections.Computer Research and Modeling14June 2022, 619 - 645
  HALDOIback to text
• 24 articleT.Thomas Lepoutre and N.Nicolas Meunier. Analysis of a model of cell crawling migration.Communications in Mathematical Sciences2062022, 1589-1611
  HALDOIback to text
• 25 articleH.Helena Todorov, M.Margaux Prieux, D.Daphne Laubreton, M.Matteo Bouvier, S.Shaoying Wang, S.Simon de Bernard, C.Christophe Arpin, R.Robrecht Cannoodt, W.Wouter Saelens, A.Arnaud Bonnaffoux, O.Olivier Gandrillon, F.Fabien Crauste, Y.Yvan Saeys and J.Jacqueline Marvel. CD8 memory precursor cell generation is a continuous process.iScience2592022, 104927
  HALDOIback to text
• 26 articleE.Elias Ventre. Reverse engineering of a mechanistic model of gene expression using metastability and temporal dynamics.In Silico Biology143-4January 2022, 89-113
  HALDOIback to text

Doctoral dissertations and habilitation theses

• 27 thesisL.Léonard Dekens. Quantifying the influence of sexual reproduction on the spatial eco-evo dynamics of species characterized by complex traits: asymptotic methods..Université Claude Bernard Lyon IJuly 2022
  HALback to text
• 28 thesisM.Mete Demircigil. Collective Movement in Dictyostelium discoideum and Other Species. Modeling, Analysis and Simulations.Université Claude Bernard - Lyon 1; Institut Camille JordanAugust 2022
  HAL
• 29 thesisE.Elias Ventre. Analysis, calibration and evaluation of stochastic models of gene expression.Ecole normale supérieure de lyon - ENS LYONSeptember 2022
  HALback to text

Reports & preprints

• 30 miscV.Vincent Calvez, H.Hélène Hivert and H.Havva Yoldaş. Concentration in Lotka-Volterra parabolic equations: an asymptotic-preserving scheme.April 2022
  HAL
• 31 miscI.Ionel Ciuperca, L.Laurent Pujo-Menjouet, L.Leon Matar-Tine, N.Nicolas Torres and V.Vitaly Volpert. A qualitative analysis of a Aβ-monomer model with inflammation processes for Alzheimer's disease.November 2022
  HAL
• 32 miscM.Mete Demircigil. When Self-Generated Gradients interact with Expansion by Cell Division and Diffusion. Analysis of a Minimal Model.March 2022
  HAL
• 33 misc J.Jimmy Garnier, O.O Cotto, T.T Bourgeron, E.E Bouin, T.T Lepoutre, O.O Ronce and V.V Calvez. Adaptation to a changing environment: what me Normal? June 2022
  HAL
• 34 miscE.Elias Ventre, U.Ulysse Herbach, T.Thibault Espinasse, G.Gérard Benoit and O.Olivier Gandrillon. One model fits all: combining inference and simulation of gene regulatory networks.June 2022
  HALDOI