Competitive numerical analysis for stochastic HIV/AIDS epidemic model in a two‐sex population

Abstract

This study is an attempt to explain a reliable numerical analysis of a stochastic HIV/AIDS model in a two-sex population considering counselling and antiretroviral therapy (ART). The authors are comparing the solutions of the stochastic and deterministic HIV/AIDS epidemic model. Here, an endeavour has been made to explain the stochastic HIV/AIDS epidemic model is comparatively more pragmatic in contrast with the deterministic HIV/AIDS epidemic model. The effect of threshold number H * holds on the stochastic HIV/AIDS epidemic model. If H * < 1 then condition helps us to control disease in a two-sex human population while H * > 1 explains the persistence of disease in the two-sex human population. Lamentably, numerical methods such as Euler-Maruyama, stochastic Euler, and stochastic Runge-Kutta do not work for large time step sizes. The recommended structure preserving framework of the stochastic non-standard finite difference (SNSFD) scheme conserve all vital characteristics such as positivity, boundedness, and dynamical consistency defined by Mickens. The effectiveness of counselling and ART may control HIV/AIDS in a two-sex population.

Design of nonstandard computational method for stochastic susceptible–infected–treated–recovered dynamics of coronavirus model

“…Theorem 4 For any m ≥ 0, the system of discrete dynamical Eqs. (17) to (20) has the same steady states as that of the continuous dynamical Eqs. (8) to (11).…”

“…In this paper, we aim to suggest and present mathematical analysis revealing the spread of such a deathly disease, and develop some prediction with real-world data [15,16]. Also, the proposed structure-preserving nonstandard computational method, named the stochastic nonstandard finite difference (SNSFD), is applied for the given pandemic model [17,18]. This is the critical point of this paper.…”

Modeling the effect of delay strategy on transmission dynamics of HIV/AIDS disease

“…There are many models available in the literature, which exhibit the dynamics of this disease by the system of nonlinear differential equations without any delay, although the delay inclusion makes the model more realistic. The dynamical behavior of the population model with time delay has now become a hot topic of research [ 2 ]. Ogunlaran et al [ 3 ] presented an effective strategy to fight against HIV infection in humans by using the compartment models.…”

A finite-difference discretization preserving the structure of solutions of a diffusive model of type-1 human immunodeficiency virus

“…Some of these models are based on ordinary differential equations, and their analytical study is followed by simulation experiments which assess the validity of the qualitative results. To that end, various numerical methodologies have been designed and analyzed, like some algorithms for simulating the HIV-1 dynamics at a cellular level [6], stem cells therapy of HIV-1 infections [7], fractional optimal control problems on HIV-1 infection of CD4 + T cells using Legendre spectral collocation [8], HIV-1 cure models with fractional derivatives which possess a nonsingular kernel [9], stochastic HIV-1/AIDS epidemic models in two-sex populations [10], among other reports [5,[11][12][13].…”