International Workshop "Mathematical modelling of epidemiological dynamics" 2024

Title: Mathematical models for glial cells

Abstract: Our aim in this talk is to discuss mathematical models describing energetic mechanisms in the brain. We will in particular focus on a Cahn-Hilliard type model for which we will prove the existence of a global in time model.

Title: Generation of analytic semigroups for a generalized evolution problem in population dynamics

Abstract: We study a generalized diffusion problem, in population dynamics, set in a cylindrical open domain \(\Omega = (a,b)\times\omega\), where \(\omega\) is a regular open set of \(\mathbb{R}^{n-1}\). The term "generalized diffusion" here means that the spatial diffusion is written as a linear combination of the Laplacian and the Bilaplacian. The biharmonic term models the dispersion induced by long-range interactions (in the neighborhood of the neighborhood). This work is inspired by the study carried out in [1]. Let \(T > 0\). We study the following evolution problem: \begin{equation*} \left\{\hspace{-0.1cm}\begin{array}{llll} \dfrac{\partial u}{\partial t} (t,x,y) + \Delta^2 u(t,x,y) - k \Delta u(t,x,y) &\hspace{-0.1cm} = &\hspace{-0.1cm} f(t,x,y), & t \in (0,T],~x \in (a,b), ~y \in \omega, \\ u(t,x,\zeta) = \Delta u (t,x,\zeta) &\hspace{-0.1cm}=&\hspace{-0.1cm} 0, & t \in (0,T],~x \in (a,b),~\zeta \in \partial\omega \\ u(t,a,y) = u(t,b,y) = \dfrac{\partial u}{\partial x}(t,a,y) = \dfrac{\partial u}{\partial x}(t,b,y) &\hspace{-0.1cm} = &\hspace{-0.1cm} 0, & t \in (0,T],~y \in \omega \\ u(0,x,y) &\hspace{-0.1cm}=&\hspace{-0.1cm} u_0(x,y), & x\hspace{-0.075cm} \in (a,b),~y \in \omega, \end{array}\right. \end{equation*} where \(k \in \mathbb{R}\), \(f \in L^p((0,T)\times \Omega)\), \(p\in (1,+\infty)\) and \(u\) is a population density.
The study of this problem structured in time and space is carried out within the general framework of Banach spaces constructed on \(L^p\) spaces. To this end, we study the spectral properties of the following generalized diffusion operator: $$\left\{\begin{array}{ccl} D(\mathcal{A}) & = & \left\{\varphi \in W^{4,p}(\Omega) \cap W^{1,p}_0 (\Omega): \Delta \varphi = 0 \text{ on }(a,b) \times \partial\omega \text{ and }\dfrac{\partial \varphi}{\partial x} = 0 \text{ on }\{a,b\}\times\omega\right\}\\ \mathcal{A} \varphi & = & -\Delta^2 \varphi + k \Delta \varphi, \quad \varphi \in D(\mathcal{B}). \end{array}\right.$$ The previous PDE problem is then rewritten as the following abstract Cauchy problem: $$\left\{\begin{array}{l} u'(t) - \mathcal{A} u(t) = f(t), \quad t \in (0,T] \\ u(0) = u_0, \end{array}\right.$$ where \(u(t)(.) := u(t,.)\) and \(f(t)(.):= f(t,.)\) with \(f \in L^p(0,T;L^p(\Omega))\).
We study the spectral properties of the diffusion operator in order to show that it generates an analytical semigroup. We then show the existence and uniqueness of the solution of the abstract Cauchy problem which enjoys the maximal regularity property if and only if \(u_0\) is in a suitable real interpolation space, see [4]. Among other things, we use [2], [3], [5].
This study mainly uses the theory of analytic semigroups, the real interpolation theory, the functional calculus, the theory of UMD Banach spaces and that of operators with Bounded Imaginary Powers (BIP operators).

Références
[1] D.S. Cohen & J.D. Murray, A generalized diusion model for growth and dispersal in population, Journal of Mathematical Biology, 12, Springer-Verlag, 1981, pp. 237-249.
[2] G. Dore & A. Venni, On the closedness of the sum of two closed operators, Math. Z., 196 (1987), 189-201.
[3] R. Labbas, S. Maingot, D. Manceau & A. Thorel, On the regularity of a generalized diusion problem arising in population dynamics set in a cylindrical domain, J. Math. Anal. Appl., 450 (2017), 351-376.
[4] R. Labbas, S. Maingot & A. Thorel, Generation of analytic semigroup for some generalized diffusion operators in Lp-spaces, Math. Ann., 384 (2022), 913-961.
[5] A. Thorel, Operational approach for biharmonic equations in Lp-spaces, J. Evol. Equ., 20 (2020), 631-657.

Title: On the global dynamics of a size-structured population model.

Abstract: We study a model recently proposed by C. Barril et al. which describes the dynamics of a population organized hierarchically with respect to size. The model consists of a scalar nonlinear renewal equation \(\phi(t) = \mathfrak{F}\phi_t\) over the weighted space \(L^1_\rho(\mathbb{R}_-)\). We analyse how the stability and persistence properties of the delayed model can be deduced from the associated one-dimensional map \(F(b) = \mathfrak{F}b\), \(b\in \mathbb{R}_+\). In particular, under relatively weak assumptions on reproduction, death and growth rates, \(\beta,~ \mu\) and \(g\), we prove that the associated semiflow possesses a global compact attractor of points. In addition, we consider two special cases: a) the reproduction rate \(\beta\) is an increasing function of trees height; b) the growth rate \(g\) of an individual is a strictly decreasing function. In particular, case a) implies that the associated semiflow is monotone while in case b) this is of monotone positive feedback type.

Title: A Newtonian approach to the dynamics of the spread of high-risk infectious diseases.

Title: Slowing positive feedback effect and partial infertility: how does it affect on the stability of a SIR epidemic model

Abstract: Positive feedback effect is a type of regulation in biological systems in which the end product of a process in turn increases the stimulus of that same process. Partial fertility is an important phenomenon to include in epidemic models, where epidemics tend to decrease population densities.
In this work, we study the dynamical behavior of a modified SIR epidemiological model by introducing positive feedback and partial infertility effects. Controlling the reproduction rate is considered by the addition of slow feedback effect given by an exponent and the infertility by a fraction, both influencing pandemics. An analytic expression of replacement ratios that depend on the effects are determined. The results obtained show that the local stability of the disease-free equilibrium is determined by the value of a certain threshold parameter called the basic reproductive number \(R_0\) and the local stability of the free disease equilibrium depends on the replacement ratios. A Hopf bifurcation is analytically verified for the exponent. The qualitative analysis shows that the slowing feedback exponent promotes more changes to the propagation of the disease than other parameters. Finally, the sensitivity analysis and simulations show the efficiency of the feedback and infertility on an epidemics model.
References
[1] LÓPEZ-CRUZ, R. Implications of the delayed feedback effect on the stability of a SIR epidemic model. Selecciones Matemáticas, 10(01), 29-40. (2023).
[2] LÓPEZ-CRUZ R. Global stability of an SAIRD epidemiological model with negative feedback. Advances in Continuous and Discrete Models. 2022 May 12;2022(1):41.
[3] LV Y, CHEN L, CHEN F, LI Z. Stability and bifurcation in an SI epidemic model with additive Allee effect and time delay. International Journal of Bifurcation and Chaos. 2021 Mar 30;31(04):2150060.
[4] KUMAR A. AND NILAM Stability of a Time Delayed SIR Epidemic Model Along with Nonlinear Incidence Rate and Holling Type-II Treatment Rate, International Journal of Computational Methods, Vol. 15, No. 1 (2018)
[5] ALFARO, M. Slowing Allee effect versus accelerating heavy tails in monostable reaction diffusion equations. Nonlinearity, 30(2), 687. (2017).

Title: Fractionation by Diffusion in heterogeneous environments

Abstract: In this lecture, we investigate the phenomenon of particle fractionation in heterogeneous environments. As can be easily predicted, in the homogeneous case the particles spread out evenly and a constant equilibrium is naturally expected due to the nature of the diffusion phenomenon. However, there is a lot of experimental data showing particle fractionation in heterogeneous environments even without external forces. We introduce the heterogeneous diffusion equation, derived from a microscopic model, which provides a new framework for understanding heterogeneous diffusion. We will examine the equations for two cases: varying solvent density and temperature gradient.

Title: Mathematical modelling of respiratory viral infections

Abstract: In this lecture we will present an overview of recent works on mathematical modelling of respiratory viral infections. We will begin with the investigation of infection progression in cell cultures and in tissues of human body. We will determine viral load and infection spreading speed and we will apply these results to evaluate infectivity and severity of symptoms for different variants of the SARS-CoV-2 infection. In the second part of the presentation, we will discuss some novel models of the epidemic progression in the population.

Title: Parameter Estimation for a Disease Transmission Model from a Reservoir with Thresholding.

Abstract: Transmission of disease to a primary population of interest from a disease reservoir of may be fairly rare when the number of such infected organisms of the reservoir is small but may qualitatively increase as the number rises. To model such a scenario, a birth-death process is proposed to model the unobserved population size of infected organisms of the reservoir. This model then considers the transmission effect to a second species, by defining a stochastic process based on the infected reservoir size. The third element of the model assumes a threshold for the reservoir size beyond which a higher transmission rate of infection is realized. A maximum likelihood procedure is developed for this model which combines the EM algorithm using a particle filter to enable the expectation step.

Title: Insights on dengue fever dynamics models: the influence of mosquito and disease biological features

Abstract: Mathematical models play a crucial role in assisting public health authorities in making timely decisions for disease forecast or control. For vector-borne diseases, integrating host and vector dynamics into models can lead to high analytical complexity, and also validation challenging, mainly due to limited data regarding vector populations.
In this talk, two compartmental models akin to the SIR type were developed to characterize vector-borne infectious disease dynamics. Motivated by dengue fever epidemiology, the models varied in their treatment of vector dynamics, one with implicit vector dynamics and the other explicitly modeling mosquito-host contact. The models incorporate fundamental biological features, such as distinctions between primary and secondary infections, as well as considerations of temporary immunity following a primary infection and disease enhancement in subsequent infections, analogous to the temporary cross-immunity and the Antibody-dependent enhancement biological processes observed in dengue epidemiology. Without considering the strain structure of pathogens, we perform a detailed qualitative analysis of these models using bifurcation theory, aiming to assess the extent to which these biological mechanisms can generate complex behavior in simple epidemiological models. The results offers valuable insights into the influence of variables and parameters commonly used in dengue modeling and underscores the importance of using simple models for modeling analysis.

Title: Biological populations as stationary distributions in the space of genotypes

Abstract: We develop a new model describing population density distribution with respect to genotype considered as a continuous variable. The model represents a reaction-diffusion equation with a special drift term arising due to random mutations of the genotype. We prove the existence and stability of a continuous family of positive stationary solutions of this equation decaying at infinity. The minimal solution of this family resembles a normal distribution with over-exponential decay rate, while all other solutions have a polynomial decay. Furthermore, the minimal, quasi-normal, symmetric stationary solution is an obligatory ultimate destination for each evolutionary process starting with the realistic compact initial data.
This communication is based on a joint work with Vitaly Volpert, University Lyon 1 and Boris Peña y Lillo, Universidad del Bio-Bio, Chile.

Title: Pattern dynamics appearing on compact metric graph

Abstract: The study of reaction-diffusion equations on metric graph has been drawing attention recently. Here, we focus on pattern dynamics on compact metric graphs. There are eight different types of compact metric graphs which are constructed from two or three finite intervals. And we consider systems of reaction-diffusion equations on these compact metric graphs with natural boundary conditions. Suppose additionally the system has Turing or Wave instability. Then, by choosing the length of the segment intervals appropriately we have a degenerate situation, where we can use Fourier expansion. This enables us the normal form analysis to determine the local bifurcation structure around the bifurcation point.

Title: Analysis of a macroscopic spatio-temporal pedestrian PDE model for a population in a danger situation.

Abstract: In this talk, we present some pedestrian PDE models describing the spatio-temporal dynamics of a population under different human behaviors (e.g. alert, panic and control) during a catastrophic event. We propose a macroscopic first-order compartmental advection-diffusion model. For this model, using semigroup theory, we prove the local existence, uniqueness and regularity of a solution, as well as the positivity and boundedness \(L^1\) of this solution. Then, in order to study the spatio-temporal propagation of these behavioural reactions within a population during a catastrophic event, we present several numerical simulations for different evacuation scenarios. Finally, as a perspective, we discuss a second-order macroscopic model involving a population in a panic situation.
References:
[1] K. Khalil, V. Lanza, D. Manceau, M. A. Aziz-Alaoui & D. Provitolo, Analysis of a spatio-temporal advection-diffusion model for human behaviors during a catastrophic event, Mathematical Models and Methods in Applied Sciences (M3AS) Journal, 34(07), 1309--1342 (2024).

Title: Generalized weak positive feedback effect on the stability of a SIR epidemic model

Abstract: This work aims to study the dynamical behavior of a SIR model by introducing a weak positive feedback effect in the growth rate. This effect is generalized using a fractional exponent in the growth rate, which allows us to introduce a family of functions that can control the acceleration of the growth. The SIR model was studying considering a change of parameters that became it into a two variable system, after that the existence of three equilibrium points as maximum and we study their local stability. The expression for the basic reproduction number was determined, and the forward bifurcation respect to this epidemiological parameter is shown. Moreover, the existence of Hopf bifurcation related to the fractional exponent was found. Finally, the findings are shown using computational simulations.
References:
[1] Alfaro, M. (2017). Slowing Allee effect versus accelerating heavy tails in monostable reaction diffusion equations. Nonlinearity, 30(2), 687.
[2] Castillo-Chavez, C., & Song, B. (2004). Dynamical models of tuberculosis and their applications. Math. Biosci. Eng, 1(2), 361-404.
[3] Guckenheimer, J., & Holmes, P. (1982). Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Applied Mathematical Sciences.
[4] Kuznetsov, Y. A., & Kuznetsov, Y. A. (2004). Numerical analysis of bifurcations. Elements of applied bifurcation theory, 505-585.
[5] Perko, L. (2013). Differential equations and dynamical systems (Vol. 7). Springer Science & Business Media.

Title: Características epidemiológicas de Leptospirosis en Colombia, 2012-2022: Estudio epidemiológico.

Abstract:
Contextualización: El número de nuevos casos de leptospirosis en Colombia sigue siendo alto. Leptospira interrogans es una bacteria patogénica para hombres y animales, con más de 200 variedades serológicas. La leptospirosis es una enfermedad zoonótica, es común el registro de infección en humanos por consumo de alimentos contaminados por la orina de ratones, su presencia es endémica en países húmedos tropicales y se da después de la presencia de lluvias. El diagnóstico es generalmente basado en la serología junto con una presentación clínica y datos epidemiológicos (antecedentes de exposición, presencia de factores de riesgo), existen registros de casos clínicos comprobados de muestras aisladas por métodos de PCR (o clásicos) en Colombia en el periodo de 2012-2022. ¿Han cambiado la incidencia y las características epidemiológicas de la Leptospirosis en Colombia de 2012 a 2022? La hipótesis es que pueden tener una probabilidad significativa de riesgo factores ambientales como: saneamiento débil, inseguridad alimentaria alta, grupos de edad vulnerables, inundaciones y desbordamiento, contaminación generalizada del agua.
Objetivo: El objetivo de este estudio fue caracterizar la tendencia epidemiología reciente de la leptospirosis en Colombia con base en los datos de vigilancia nacional.
Materiales y métodos: Este estudio transversal recopiló datos demográficos (sexo, edad, ocupación, origen étnico y departamento de residencia), fecha de inicio de la enfermedad, fecha de diagnóstico y resultados clínicos de todos los pacientes informados en el Sistema de Vigilancia en Salud Pública- SIVIGILA- del Ministerio de Salud y Protección Social de Colombia, desde el 1 de enero de 2012 hasta el 31 de diciembre de 2022, así como también algunas otras fuentes de datos sobre información nacional.
Se utilizó para explorar la localización, distribución y variabilidad geográfica y temporal el modelo multivariante jerárquico de Poisson que modela simultáneamente la correlación espacial y temporal centrándose en la incidencia, los patrones temporales y geográficos. Se utilizó análisis de regresión logística para encontrar los factores de riesgo de leptospirosis.
Resultados esperados: Se espera por medio de este estudio realizar un análisis integral, sistemático y más profundo de la Leptospirosis en Colombia, que proporcione una base científica para la formulación de estrategias de prevención y control de la leptospirosis.

Title: An evolutionary epidemiological model with environmental and human-to-human contamination

Abstract: A system of PDE equations describing the phenotypic adaptations of a pathogen through multiple pathways of contamination (direct or indirect through environmental contact) is considered. The mutation process is described using a non-local discrete operator in the phenotype space. The existence of non-trivial spatial-homogeneous steady states is shown. Threshold conditions, linked with the reducible properties of the non spatial characteristic matrix are defined to determine the existence, at steady state, of all traits or just part of them. The link between reducible properties of the characteristic matrix and the irreversibility of the mutation process is studied. In the irreductible case, we prove the existence of travelling wave solutions, which take the role of epidemic fronts, and describe their structure with respect to the phenotypic variable.

Title: Implications of a positive feedback effect on the stability of a SIR epidemic model

Abstract A basic mathematical model in epidemiology is the SIR (Susceptible–Infected–Removed) model, which is commonly used to characterize and study the dynamics of the spread of some infectious diseases. In humans, the time scale of a disease can be short and not necessarily fatal, but in some animals (for example, insects), this same short time scale can make the disease fatal if we take into account their life expectancy.
In this work, we will see how a positive feedback effect (decrease of the susceptible population at small densities) in the growth rate and partial infertility on the infected people in a SIR model can cause a qualitative characterization of the dynamics defined by the original SIR model. Finally, we will also show with numerical simulations how the effects cause very interesting qualitative changes of the system with epidemiological significance.
References
[1] LÓPEZ-CRUZ, R. Implications of the delayed feedback effect on the stability of a SIR epidemic model. Selecciones Matemáticas, 10(01), 29-40. (2023).
[2] USAINI, S., LLOYD, A. L., Anguelov, R., & Garba, S. M. (2017). Dynamical behavior of an epidemiological model with a demographic Allee effect. Mathematics and Computers in Simulation, 133, 311-325

Title: Less effective, but individually less costly, prophylactic measures can reduce disease prevalence in a very simple epidemic model accounting for human behaviour

Abstract: We study a simple SIS epidemic model accounting for human behaviour. Individuals can decide at each instant of time whether or not they adopt prophylactic (hereafter protection) measures such as mask wearing or social distancing. These measures decrease susceptibility and/or transmission. We consider a situation in which individuals are unaware of their current health status (infected or not), but can perceive disease prevalence at the population level. This assumption fits situations in which tests are not widely available. Thus, personnal decisions depend first on disease prevalence, as a proxy for the risk of being infected or infecting others, and second on the fraction of the population complying to the protection measure, which people can observe in their every day life. Human behaviour is assumed to be driven by imitation dynamics (Bauch, 2005; Poletti et al., 2009). When the disease does not naturally die out, the model has three types of endemic equilibria: no-protection, mixed-protection, and full-protection. Which endemic equilibrium is stable depends on the parameter values. We assume that the efficiency of the protection measure is positively correlated to its individual cost. Increasing the efficiency of the protection measure and therefore its individual cost can make the system switch from full protection to mixed-protection. This way, increasing the efficiency of a protection measure may increase disease prevalence at equilibrium. In other words, disease prevalence is minimized for intermediate efficiency, and individual cost, of the prophylactic measure. The rational is that when the prophylactic measure is too effective and therefore costly, part of the population free-rides on the effort of others and drops protection, resulting in increased prevalence. Altogether, our results show that the interplay between epidemiology and human behaviour may lead to counterintuitive but nevertheless intelligible outcomes, that should be anticipated when designing public health policies.
This work is shared with François Castella and Frédéric Hamelin.
Bauch, C. T. (2005). Imitation dynamics predict vaccinating behaviour. Proceedings of the Royal Society B: Biological Sciences, 272 (1573), 1669-1675.
Poletti , P. et al. (2009) Spontaneous behavioural changes in response to epidemics. Journal of Theoretical Biology, 260

Title: Modelación de la variación espacio-temporal de la hepatitis a en Colombia.

Abstract:
Contextualization: Hepatitis A is a liver disease caused by the Hepatovirus A virus (HAV), which is transmitted mainly through the action of ingesting food or water contaminated by fluids that contain the virus transmitted by an infected person or either by direct contact with that infected person. It is estimated that almost one and a half million cases of HAV occur annually in the world, especially in countries where the disease is medium or highly endemic, such as Africa, Asia, Central and South America, and some countries in Eastern Europe. For its part, in countries like Colombia, there is an intermediate endemicity, in which there are regions with a greater presence than others, this due to problems associated with low levels of sanitation and waste management, poor food security and low supply of drinking water.
Objective: the objective of this study is to model the spatio-temporal variation of HAV in Colombia using a Bayesian regression model that integrates the association with sociodemographic, environmental and climatic factors and the dynamic variables of space and time.
Materials and methods: In this study, in order to model the spatio-temporal variation of HAV in Colombia, use will be made of the database of patients confirmed with hepatitis A obtained through the Public Health Surveillance System-SIVIGILA-. from the Ministry of Health and Social Protection of Colombia, as well as some other data sources on national information. For which data preprocessing will be carried out, given that this phase is of vital importance for the correct functioning of the algorithms. The methodological structure is based on a descriptive analysis in three dimensions: 1. risk factors associated with the disease; 2. the behavior over time of hepatitis A cases; 3. the behavior in space of hepatitis A cases. To later give way to the proposal of a space-time Bayesian regression model.
Expected results: Through this study, it is expected to use statistical modeling and data science tools to extract significant information for the health and food safety field that can be useful for decision making.

Title: Stability of the trivial equilibrium in degenerate monostable reaction-diffusion equations.

Abstract: This talk adresses the long-term behavior of reaction-diffusion equations \(\partial_{t} u = \Delta u + f(u)\) in \(\mathbb{R}^{N}\), where the growth function \(f\) behaves as \(u^{1+p}\) when \(u\) is near the origin. Specifically, we are interested in the persistance versus extinction phenomena in a population dynamics context, where the function \(u\) represents a density of individuals distributed in space. The degenerated behavior \(f(u)\sim u^{1+p}\) near the null equilibrium models the so-called Allee effect, which penalizes the growth of the population when the density is low. This effect simulates factors such as inbreeding, mating difficulties, or reduced resistance to extreme climatic events. We will begin the presentation by discussing a result linking the questions of persistence and extinction with the dimension \(N\) and the intensity of the Allee effect \(p\), as established in the classical paper by Aronson and Weinberger (1978). This result is closely related to the seminal work of Fujita (1966) on blow-up versus global existence of solutions to the superlinear equation \(\partial_{t}u = \Delta u + u^{1+p}\). Following these preliminary results, we will focus on a reaction-diffusion system involving a "heat exchanger", where the unknowns are coupled through the diffusion process, integrating super-linear and non-coupling reactions. An analysis of the solution frequencies for the purely diffusive heat exchanger will allow us to estimate its "dispersal intensity", which is a key information for addressing blow-up versus global existence in such semi-linear problems. This work represents a first step toward Fujita-type results for systems coupled by diffusion and raises several open questions, particularly regarding the exploration of more intricate diffusion mechanisms.

Title: How to use the SIR model to validate epidemic prevention policies

Abstract: Various epidemic models have been mainly used to predict how far an epidemic will spread in the future. However, epidemic models based on the ODE system have limitations in prediction. Additionally, when epidemic prevention measures are implemented, the coefficients of the model fundamentally change. In this presentation, we will present the use of the SIR model not as a prediction but as a means of verifying the effectiveness of epidemic prevention measures. The basic idea is to verify how the basic reproduction number R_0 of the model reflects specific policy changes through appropriate stochastic individual-based models.

Title: Hommage to Pierre Magal

Abstract: As a short review we successively present the methods for phenomenological modeling of the evolution of reported and unreported cases of COVID-19, both in the exponential phase of growth and then in a complete epidemic wave. After the case of an isolated wave, we present the modeling of several successive waves separated by endemic stationary periods. Then, we treat the case of multi-compartmental models without or with age structure. Eventually, we review the literature, based on 230 articles selected in 11 sections, ranging from the medical survey of hospital cases to forecasting the dynamics of new cases in the general population.

This review favors the phenomenological approach over the mechanistic approach in the choice of references and provides simulations of the evolution of the number of observed cases of COVID-19 for only 10 states (California, China, France, India, Israel, Japan, New York, Peru, Spain and United Kingdom).

References:
Z. XU, D. WEI, Q. ZENG, H. ZHANG, Y. SUN & J. DEMONGEOT
More or less deadly? A mathematical model that predicts 1 SARS-CoV-2 evolutionary direction.
Computers in Biology & Medicine, 153, 106510 (2023).
J. DEMONGEOT & P. MAGAL
Data Driven Modeling in Mathematical Biology.
Frontiers in Applied Maths & Statistics, 9, 1129749 (2023).
Z. XU, D. YANG, H. ZHANG & J. DEMONGEOT
A Novel Mathematical Model that Predicts the Protection Time of SARS-CoV-2 Antibodies.
Viruses, 15, 586 (2023).
Z. XU, Q. PENG, W. LIU, J. DEMONGEOT, D. WEI
Antibody Dynamics Simulation - A Mathematical Exploration of Clonal Deletion and Somatic Hypermutation.
Biomedicines, 11, 2048 (2023)
J. WAKU, K. OSHINUBI, U.M. ADAM & J. DEMONGEOT
Forecasting the endemic/epidemic transition in COVID-19 in some countries: influence of the vaccination.
Diseases, 11, 135 (2023).
K. OSHINUBI, P. MAGAL, O.B. LONGE & J. DEMONGEOT
Editorial: Mathematical and statistical modeling of infection and transmission dynamics of viral diseases.
Frontiers in Public Health, 11, 2023 (2023).
J. DEMONGEOT & P. MAGAL
Population dynamics model for aging
AIMS MBE, 20, 19636–1966. (2023). arXiv:2309.17106 (2023).
J. DEMONGEOT, Q. GRIETTE, Y. MADAY & P. MAGAL
A Kermack-McKendrick model with age of infection starting from a single or multiple cohorts of infected patients.
Proc. Royal Society A, 479, 2022.0381 (2023).
J. DEMONGEOT, P. MAGAL & K. OSHINUBI
Forecasting the changes between endemic and epidemic phases of a contagious disease, with example of COVID-19.
Mathematical Medicine & Biology (accepted). arXiv:2309.17026 (2023).
B. KAMMEGNE, K. OSHINUBI, T. BABASOLA, O.J. PETER, O.B. LONGE, R.B. OGUNRINDE, E.O. TITILOYE & J. DEMONGEOT
Mathematical modelling of spatial distribution of COVID-19 outbreak using diffusion equation.
Pathogens, 12, 88 (2023).
Z. XU, J. SONG, H. ZHANG, Z. WEI, D. WEI & J. DEMONGEOT
Mathematical Modeling of Host-Virus Interaction in Dengue Virus Infection: A Quantitative Study.
Viruses, 16, 216 (2024).
Z. XU, Q. PENG, J. SONG, H. ZHANG, D. WEI, J. DEMONGEOT & Q. ZENG
Bioinformatic analysis of defective viral genomes in SARS-CoV-2 and its impact on population infection characteristics.
Frontiers in Immunology, 15, 1341906 (2024).
Z. XU, Q. PENG, J. SONG, H. ZHANG, Z. WEI, D. WEI, J. DEMONGEOT & Q. ZENG
A Mathematical Model Simulating the Adaptive Immune Response in Various Vaccines and Vaccination Strategies.
Infectious Disease Modelling (submitted). MedRxiv, doi.org/10.1101/2023.10.05.23296578 (2023).
J. DEMONGEOT & P. MAGAL
Data-Driven Mathematical Modeling Approaches for COVID-19: a survey.
Physics of Life Reviews (submitted). ArXiv, doi.org/10.48550/arXiv.2309.17087 (2023).