This work is the numerical analysis and computational companion of the paper by Kamgang and Sallet (Math. Biosc. 213 (2008), pp. 1–12) where threshold conditions for epidemiological models and the global stability of the disease-free equilibrium (DFE) are studied. We establish a discrete counterpart of the main continuous result that guarantees the global asymptotic stability (GAS) of the DFE f...

This paper is concerned with the construction and developing of several nonstandard finite difference (NSFD) schemes in matrix form in order to obtain numerical solutions of epidemic models. In particular, we deal with a classical SIR epidemic model and a seasonal model associated with the evolution of the transmission of respiratory syncytial virus RSV in the human population. The first model ...

The aim of this paper is to design appropriate nonstandard finite difference (NSFD) schemes for two population mathematical models based on coupled nonlinear ordinary differential equations. Our work clarifies existing constructions NSFD these models, which are not in full compliance with Mickens' methodology. We select the denominator functions discrete first-order derivatives depending existe...

In this paper, we derive a discretized multi-group epidemic model with time delay by using a nonstandard finite difference (NSFD) scheme. A crucial observation regarding the advantage of the NSFD scheme is that the positivity and boundedness of solutions of the continuous model are preserved. Furthermore, we show that the discrete model has the same equilibria, and the conditions for their stab...

‎In this paper‎, ‎we introduce fractional-order into a model of HIV-1 infection of CD4^+ T--cells‎. ‎We study the effect of ‎the changing the average number of viral particles $N$ with different sets of initial conditions on the dynamics of‎ ‎the presented model‎. ‎ ‎The nonstandard finite difference (NSFD) scheme is implemented‎ ‎to study the dynamic behaviors in the fractional--order HIV-1‎ ‎...

In the present paper, SIR model with nonlinear recovery and Monod type equation as incidence rates is proposed analyzed. The expression for basic reproduction number obtained which plays a main role in stability of disease-free endemic equilibria. nonstandard finite difference (NSFD) scheme constructed denominator function chosen such that suggested ensures solutions boundedness. It shown NSFD ...

Fuzziness or uncertainties arise due to insufficient knowledge, experimental errors, operating conditions and parameters that provide inaccurate information. The concepts of susceptible, infectious recovered are uncertain the different degrees in susceptibility, infectivity recovery among individuals population. differences can arise, when population groups under consideration having distinct h...

Abstract— The aim of this work is to construct high-order numerical schemes that preserve the dynamical properties a mathematical model describing spread computer viruses on Internet. For purpose, we first apply Mickens’ methodology formulate dynamically consistent nonstandard finite difference (NSFD) scheme for under consid­eration. After that, constructed NSFD combined with Richardson’s extra...