Related papers: Bifurcation analysis for a SIRS model with a nonli…
The aim of this paper is to study the dynamics of a reaction--diffusion SIS (susceptible-infectious-susceptible) epidemic model with a nonlinear incidence rate describing the transmission of a communicable disease between individuals. We…
In this paper, we study an analytically tractable SIS model with a non-linear incidence rate for the number of infectious individuals described through a stochastic differential equation (SDE). We guarantee the existence of a positive…
We construct an SIR-type model for COVID-19, incorporating as a parameter the susceptible individuals' cautiousness level. We determine the model's basic reproduction number, study the stability of the equilibria analytically, and perform a…
We study the Suscectible-Infected-Recovered-Susceptible (SIRS) epidemic model on deterministic networks. For connected but otherwise general interaction patterns and heterogeneous recovery and loss-of-immunity rates, we identify a…
SIRS models capture transmission dynamics of infectious diseases for which immunity is not lifelong. Extending these models by a W compartment for individuals with waning immunity, the boosting of the immune system upon repeated exposure…
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…
This paper studies qualitative properties of solutions of nonlocal infectious SIR epidemic models (1.3)-(1.5), with the homogeneous Neumann boundary conditions, Dirichlet boundary conditions and free boundary, respectively. We first use the…
In the present work, we have introduced and studied two epidemic models that are constructed with Caputo fractional derivative. We considered standard incidence rate and varying population dynamics for SIS and SIRS mathematical models.…
This paper conducts research on the established model and presents the main conclusions . Firstly, by separately considering the infectivity of each of the two infectious diseases and the infectivity of the population simultaneously…
The SIR model is a three-compartment model of the time development of an epidemic. After normalizing the dependent variables, the model is a system of two non-linear differential equations for the susceptible proportion $S$ and the infected…
We performed a thorough sensitivity analysis of the herd immunity threshold for discrete-time SIR compartmental models with a static network structure. We find unexpectedly that these models violate classical intuition which holds that the…
In this paper, we are concerned with the stochastic susceptible-infectious-susceptible (SIS) epidemic model on the complete graph with $n$ vertices. This model has two parameters, which are the infection rate and the recovery rate. By…
This paper analyses the dynamics of infectious disease with a concurrent spread of disease awareness. The model includes local awareness due to contacts with aware individuals, as well as global awareness due to reported cases of infection…
In this paper, we study a stochastic susceptible-infected-susceptible (SIS) epidemic model that includes an additional immigration process. In the presence of multiplicative noise, generated by environmental perturbations, the model…
This paper focuses on and analyzes realistic SIR models that take stochasticity into account. The proposed systems are applicable to most incidence rates that are used in the literature including the bilinear incidence rate, the…
There are few adapted SIR models in the literature that combine vaccination and logistic growth. In this article, we study bifurcations of a SIR model where the class of Susceptible individuals grows logistically and has been subject to…
We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the…
Models for resident infectious diseases, like the SIRS model, may settle into an endemic state with constant numbers of susceptible ($S$), infected ($I$) and recovered ($R$) individuals, where recovered individuals attain a temporary…
This paper is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Dirichlet boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous. We…
We make a mathematical analysis of an age structured HIV infection model with both virus-to-cell and cell-to-cell transmissions to understand the dynamical behavior of HIV infection in vivo. In the model, we consider the proliferation of…