Related papers: A consistent discrete version of a non-autonomous …
The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…
Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 50's with the KiSS (after Kierstead, Slobodkin…
For a susceptible-infectious-susceptible (SIS) infection model in a heterogeneous population, we present simple formulae giving the leading-order asymptotic (large population) behaviour of the mean persistence time, from an endemic state to…
The existence and local stability of some non-negative equilibrium points of a class of SIRS infectious disease models with non-linear infection and treatment rates are investigated under the condition that the total population is a…
In this paper we analyze a continuous-time epidemic model and its discrete counterpart, where infection spreads both horizontally and vertically. We consider three cases: model with horizontal and imperfect vertical transmissions, model…
As the main contribution, this document provides a consistent discretization of a class of fixed-time stable systems, namely predefined-time stable systems. In the unperturbed case, the proposed approach allows obtaining not only a…
In this paper we study the diffusion of an SIS-type epidemics on a network under the presence of a random environment, that enters in the definition of the infection rates of the nodes. Accordingly, we model the infection rates in the form…
Many biological systems are governed by difference equations and exhibit discrete-time dynamics. Examples include the size of a population when generations are non-overlapping, and the incidence of a disease when infections are recorded at…
An integrable discretization of the SIR model with vaccination is proposed. The conserved quantities of the continuous model are inherited to the discrete model through the discretization, since the discretization is based on the…
We will study a mathematical model of the human immunodeficiency virus (HIV) infection in the presence of combination therapy that includes within-host infectious dynamics. The deterministic model requires us to analyze asymptotic stability…
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…
In this paper, an epidemic model with spatial dependence is studied and results regarding its stability and numerical approximation are presented. We consider a generalization of the original Kermack and McKendrick model in which the size…
In the Staged Progression (SP) epidemic models, infected individuals are classified into a suitable number of states. The goal of these models is to describe as closely as possible the effect of differences in infectiousness exhibited by…
We study a discrete Susceptible-Infected-Recovered (SIR) model for the spread of infectious disease on a homogeneous tree and the limit behavior of the model in the case when the tree vertex degree tends to infinity. We obtain the…
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…
Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular…
We study a stochastic SIS (susceptible-infected-susceptible) epidemic dynamics on network, under the effect of a Markovian regime-switching. We first prove the existence of a unique global positive solution, and find a positive invariant…
In this work, we derive a nonstandard finite difference scheme for the SICA (Susceptible-Infected-Chronic-AIDS) model and analyze the dynamical properties of the discretized system. We prove that the discretized model is dynamically…
In this paper we study a discrete-time SIS (susceptible-infected-susceptible) model, where the infection and healing parameters and the underlying network may change over time. We provide conditions for the model to be well-defined and…
We construct a nonstandard finite difference (NSFD) scheme for an SIRS mathematical model of respiratory virus transmission. This discretization is in full compliance with the NSFD methodology as formulated by R. E. Mickens. By use of an…