Related papers: Note on a vector-host epidemic model with spatial …
We study spaces of modelled distributions with singular behaviour near the boundary of a domain that, in the context of the theory of regularity structures, allow one to give robust solution theories for singular stochastic PDEs with…
In this paper, we consider a compartmental SIRS epidemic model with asymptomatic infection and seasonal succession, which is a periodic discontinuous differential system. The basic reproduction number $\mathcal{R}_0$ is defined and valuated…
Most epidemic models are spatially aggregate and the index which is most used for planning and policy numbers, the r number, typically refers to a single system of interest. Even if r numbers are calculated for each of adjacent areas,…
We present a modelling framework for the spreading of epidemics on temporal networks from which both the individual-based and pair-based models can be recovered. The proposed temporal pair-based model that is systematically derived from…
We study seasonal epidemic spreading in a susceptible-infected-removed-susceptible (SIRS) model on smallworld graphs. We derive a mean-field description that accurately captures the salient features of the model, most notably a phase…
Vector-borne diseases cause more than 1 million deaths annually. Estimates of epidemic risk at high spatial resolutions can enable effective public health interventions. Our goal is to identify the risk of importation of such diseases into…
We consider random perturbations of a general eco-epidemiological model. We prove the existence of a global random attractor, the persistence of susceptibles preys and provide conditions for the simultaneous extinction of infectives and…
Rapidly mutating pathogens may be able to persist in the population and reach an endemic equilibrium by escaping hosts' acquired immunity. For such diseases, multiple biological, environmental and population-level mechanisms determine the…
In current paper, we put forward a reaction-diffusion system for West Nile virus in spatial heterogeneous and time almost periodic environment with free boundaries to investigate the influences of the habitat differences and seasonal…
This paper is concerned with modeling the dynamics of social outbursts of activity, such as protests or rioting activity. In this sequel to our work in \cite{Berestycki2014}, written in collaboration with J-P. Nadal, we model the effect of…
The Covid-19 outbreak of 2020 has required many governments to develop mathematical-statistical models of the outbreak for policy and planning purposes. This work provides a tutorial on building a compartmental model using Susceptibles,…
In this paper, we study a diffusive Lotka-Volterra competition model under homogeneous Dirichlet boundary conditions. We shall discuss the effects of dispersal rate and spatial heterogeneity on population dynamics. More precisely, we…
Cholera, a severe gastrointestinal infection caused by the bacterium Vibrio cholerae, remains a major threat to public health with a yearly estimated global burden of 2.9 million cases. Although the majority of existing models for the…
We introduce and analyze several variants of a system of differential equations which model the dynamics of social outbursts, such as riots. The systems involve the coupling of an explicit variable representing the intensity of rioting…
We study an epidemic propagation between $M$ population centra. The novelty of the model is in analyzing the migration of host (remaining in the same centre) and guest (migrated to another centre) populations separately. Even in the…
In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent p-coin tosses. Spatial variants of these models are proposed, in which finite…
We study the qualitative properties of a spatial diffusive heterogeneous SIR model, that appears in mathematical epidemiology to describe the spread of an infectious disease in a population. The model we consider consists in a system of…
We consider an epidemiological SIR model with an infection rate depending on the recovered population. We establish sufficient conditions for existence, uniqueness, and stability (local and global) of endemic equilibria and consider also…
Complex contagion models that involve contagion along higher-order structures, such as simplicial complexes and hypergraphs, yield new classes of mean-field models. Interestingly, the differential equations arising from many such models…
We study extended infection fronts advancing over a spatially uniform susceptible population by solving numerically a diffusive Kermack McKendrick SIR model with a dichotomous spatially random transmission rate, in two dimensions. We find a…