Related papers: A dynamically-consistent nonstandard finite differ…
We propose a nonstandard finite difference scheme for the Susceptible-Infected-Removed (SIR) continuous model. We prove that our discretized system is dynamically consistent with its continuous counterpart and we derive its exact solution.…
We revisit the SICA (Susceptible-Infectious-Chronic-AIDS) mathematical model for transmission dynamics of the human immunodeficiency virus (HIV) with varying population size in a homogeneously mixing population. We consider SICA models…
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…
This paper introduces a nonstandard finite difference (NSFD) approach to a reaction-diffusion SEIQR epidemiological model, which captures the spatiotemporal dynamics of infectious disease transmission. Formulated as a system of semilinear…
We study the construction of a non-standard finite differences numerical scheme for a general class of two dimensional differential equations including several models in population dynamics using the idea of non-local approximation…
In this article, we construct a numerical method for a stochastic version of the Susceptible Infected Susceptible (SIS) epidemic model, expressed by a suitable stochastic differential equation (SDE), by using the semi-discrete method to a…
We propose a stochastic SICA epidemic model for HIV transmission, described by stochastic ordinary differential equations, and discuss its perturbation by environmental white noise. Existence and uniqueness of the global positive solution…
We consider a dynamical system, defined by a system of autonomous differential equations, on $\Omega\subset\mathbb{R}^n$. By using Mickens' rule on the nonlocal approximation of nonlinear terms, we construct an implicit Nonstandard Finite…
In this paper we transform a continuous-time predator-prey system with general functional response and recruitment for both species into a discrete-time model by nonstandard finite difference scheme (NSFD). The NSFD model shows complete…
A family of discrete non-autonomous SIRVS models with general incidence is obtained from a continuous family of models by applying Mickens non-standard discretization method. Conditions for the permanence and extinction of the disease and…
Relationship for dynamical properties in the vicinity of fixed points between two-dimensional continuous and its positivity-preserving discretized dynamical systems is studied. Based on linear stability analysis, we reveal the conditions…
Stability and bifurcation properties of one-dimensional discrete dynamical systems with positivity, which are derived from continuous ones by tropical discretization, are studied. The discretized time interval is introduced as a bifurcation…
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 investigate the celebrated mathematical SICA model but using fractional differential equations in order to better describe the dynamics of HIV-AIDS infection. The infection process is modelled by a general functional response and the…
In this paper we classify the pathwise asymptotic behaviour of the discretisation of a general autonomous scalar differential equation which has a unique and globally stable equilibrium. The underlying continuous equation is subjected to a…
An adequate near-optimal control problem for a stochastic SICA (Susceptible-Infected-Chronic-AIDS) compartmental epidemic model for HIV transmission with imprecise parameters is formulated and investigated. We prove some estimates for the…
In recent years, discrete fractional epidemic models with reaction-diffusion have become increasingly popular in the literature, not only for its necessity of numerical simulation, but also for its defined physical processes. In this paper,…
We propose a new dynamic SIR model that, in contrast with the available model on time scales, is biological relevant. For the new SIR model we obtain an explicit solution, we prove the asymptotic stability of the extinction and disease-free…
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 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…