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. 2019 Dec;13(6):305-315.
doi: 10.1049/iet-syb.2019.0051.

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

Ali Raza  1 , Muhammad Rafiq  2 , Dumitru Baleanu  3 , Muhammad Shoaib Arif  4 , Muhammad Naveed  4 , Kaleem Ashraf  5
Affiliations

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

Ali Raza et al. IET Syst Biol. 2019 Dec.

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.

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Figures

Fig. 1
Fig. 1
Flow diagram of the HIV/AIDS model in two sex populations
Fig. 2
Fig. 2
In the prevalence of infection in males stochastic Euler converges for h = 0.001
Fig. 3
Fig. 3
In the prevalence of infection in males, stochastic Euler shows negativity for h = 1
Fig. 4
Fig. 4
In a number of females receiving ART stochastic Euler converges for h = 0.001
Fig. 5
Fig. 5
In a number of females receiving ART stochastic Euler shows unboundedness for h = 1
Fig. 6
Fig. 6
In the prevalence of infection in males stochastic Runge Kutta converges for h = 0.001
Fig. 7
Fig. 7
In the prevalence of infection in males, stochastic Runge Kutta shows negativity for h = 2
Fig. 8
Fig. 8
In a number of females receiving ART stochastic Runge Kutta shows converges for h = 0.001
Fig. 9
Fig. 9
In a number of females receiving ART stochastic Runge Kutta shows unboundedness for h = 2
Fig. 10
Fig. 10
In the prevalence of infection in males stochastic NSFD converges for h = 0.01
Fig. 11
Fig. 11
In the prevalence of infection in males, stochastic NSFD converges for h = 100
Fig. 12
Fig. 12
In a number of females receiving ART stochastic NSFD converges for h = 0.1
Fig. 13
Fig. 13
In a number of females receiving ART stochastic NSFD converges for h = 100
Fig. 14
Fig. 14
Contrast of stochastic Euler, stochastic NSFD, deterministic and mean for h = 0.001
Fig. 15
Fig. 15
Contrast of stochastic Euler, stochastic NSFD, deterministic and mean for h = 0.9, but stochastic Euler shows negative values
Fig. 16
Fig. 16
Contrast of stochastic Runge–Kutta, stochastic NSFD, deterministic and mean for h = 0.001
Fig. 17
Fig. 17
Contrast of stochastic Runge–Kutta, stochastic NSFD, deterministic and mean for h = 2 but stochastic Runge Kutta shows negative values
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