Abstract
We develop a virus-resistant HIV-1 mathematical model with behavioural change in HIV-1 resistant non-progressors. The model hasВ both disease-free and endemic equilibrium points that are proved toВ be locally asymptotically stable depending on the value of the associated reproduction numbers. In both models, a non-linear Goh{Volterra Lyapunov function was used to prove that theВ endemic equilibrium point is globally asymptotically stable for specialВ case while the method of Castillo-Chavez was used to prove the globalВ asymptotic stability of the disease-free equilibrium point. In both theВ analytic and numerical results, this study shows that in the context ofВ resistance to HIV/AIDS, total abstinence can also play an importantВ role in protection against this notorious infectious disease.
Highlights
AMS Subject Classification: 92Bxx, 92B05. As it was reported in the 1980s, the human immunodeficiency virus (HIV), and the later stage of infection through cell depletion known as AIDS has continue to play a leading role in the series of the greatest ever infectious disease
While incorporating the behavior change in the model, we deliberately focused on the behavior change of the non-progressors HIV-1 infected individuals even though, it is imperative that all individuals can change their behavior at any given time
A non-linear Goh–Volterra Lyapunov function is used to prove that the endemic equilibrium point is globally asymptotically stable for the case when the virus-induced death rate τ = 0 while the method of Castillo-Chavez is used to prove the global asymptotic stability of the disease-free equilibrium point whenever the reproduction number is less than unity
Summary
As it was reported in the 1980s, the human immunodeficiency virus (HIV), and the later stage of infection through cell depletion known as AIDS has continue to play a leading role in the series of the greatest ever infectious disease. It is pertinent to study methods of HIV prevention Different control strategies such as behavior change due to HIV awareness campaign, reduction in sexual partners, anti retroviral treatment ART etc. Though many researchers have developed different models to examine the dynamics of the virus, HIV-1 mathematical model where infected individuals gain resistance to acquisition of HIV and resistance to deterioration of HIV incorporating behavior change in form of partial and total abstinence is still a biological question needed to be answered. Researchers like [31], [19] have done commendable work in tackling the menace of the deadly virus, in this research, we present a new virusresistant HIV-1 model with behavior change This behavior change to avoid infection happens as a result of the wide spread of the agony and death caused by HIV/AIDS.
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