Abstract
The main goal of this article is to exhibit the importance of awareness programs and travel-blocking operations, in the prevention of HIV/AIDS outbreaks, based on a multi-domains SIR epidemic model. The model devised describes the spatial-temporal spread of HIV/AIDS, in p neighboring domains, taking into account the epidemiological diversity of their populations. For a first case of the study, we focus on discussing the benefits of awareness campaigns that aim to raise public consciousness among susceptible people, about the danger of HIV/AIDS. Thus, for the reason that intra-domains interventions are not always sufficient to prevent people belonging to a domain (neighborhood, town or city for example), from a rapid expansion of HIV/AIDS, we propose the travel-blocking strategy, as a second approach presenting inter-domains interventions that health-policy makers could follow, by restricting the number of suspicious people that can participate in spreading HIV/AIDS via travel, coming from domains at high-risk of infection to enter domains with lower risk. The optimal control theory, based on Pontryagin’s maximum principle, is applied twice in this paper, for the characterizations of the awareness and travel-blocking controls. The numerical results associated to the multi-points boundary value problems are obtained based on the Forward-Backward Sweep Method combined with progressive-regressive Runge-Kutta fourth-order schemes.
Highlights
Human immunodeficiency virus infection and acquired immune deficiency syndrome (HIV/AIDS) is among epidemics that affect people either living or working in extremely poor regions of the entire terrestrial globe (, people in sub-Saharan African countries alone are living with HIV), while some important HIV/AIDS infection rates can be observed in the most affluent communities [, ]
We focus on the impact of education in HIV/AIDS based on the organization of many educational workshops and by following different awareness programs
It is essential to integrate the spatial dynamics in models that attempt to describe the spread of infectious diseases
Summary
Human immunodeficiency virus infection and acquired immune deficiency syndrome (HIV/AIDS) is among epidemics that affect people either living or working in extremely poor regions of the entire terrestrial globe ( , , people in sub-Saharan African countries alone are living with HIV), while some important HIV/AIDS infection rates can be observed in the most affluent communities [ , ]. The aim of this work is to consider an HIV/AIDS multi-domains SIR epidemic model and to set up an optimal control approach for it. In order to show the effectiveness of awareness strategies on reducing the number of HIV/AIDS infectives, a control function is introduced into the model to represent the effectiveness rate of awareness programs on susceptible population. In order to show the importance of considering the spatial spread of the epidemic, we show in the same section of simulations the influence of values of adequate contact proportions of domains at high-risk on a neighboring domain that is characterized by less risk of infection.
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