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 this paper, a mathematical model of Visceral Leishmaniasis is considered. The incorporates three populations, the human, reservoir and vector host populations. A detailed analysis presented. This reveals that undergoes backward bifurcation when associated reproduction threshold less than unity. For case where death rate due to VL negligible, disease-free equilibrium shown be globally-asympto...

This work is devoted to constructing reliable numerical schemes for some computer virus and malware propagation models. We apply the Mickens' methodology formulate nonstandard finite difference (NSFD) epidemiological models describing spread of viruses malware. Positivity, boundedness global asymptotic stability (GAS) proposed NSFD are studied rigorously. It should be emphasized that GAS establ...

Mathematical modeling is a vast field that has interdisciplinary implications for research. These models help to investigate the basic dynamics and quantitative behavior of infectious diseases affect human beings, such as COVID-19, hepatitis B virus (HBV), immunodeficiency (HIV). The current study investigates spread HBV by using model. In order determine stability disease-free endemic equilibr...

Amoebiasis is a parasitic intestinal infection caused by the highly pathogenic amoeba Entamoeba histolytica. It spread through person-to-person contact or eating drinking food water contaminated with feces. Its transmission rate depends on number of cysts present in environment. The traditional models assumed homogeneous and contradictory reality. heterogeneity its significant factor when model...

In this paper we combine nonstandard finite-difference (NSFD) schemes and Richardson’s extrapolation method to obtain numerical solutions of two biological systems. The first biological system deals with the dynamics of phytoplankton–nutrient interaction under nutrient recycling and the second one deals with the modeling of whooping cough in the human population. Since both models requires posi...

In this paper, we introduced nonstandard finite difference scheme (NSFD) for solving the continuos model with Michaelis-Menten harvesting rate. We have seen that proposed preserve local stability and positivity. Stability analysis of each fixed point discrete time has been proven. Also, numerical comparisons were made between method other methods.

Infection with human immunodeficiency virus type 1 (HIV-1) or T-lymphotropic I (HTLV-I) both can lead to mortality. CD4+T cells are the target for HTLV-I and HIV-1. In addition, HIV-1 infect macrophages. macrophages play important roles in immune system response. This article develops analyzes a discrete-time co-infection model. The model depicts within-host interaction of six compartments: uni...