Abstract
A mathematical model approach to control the spread of HIV and AIDS is needed to predict the future effect of HIV and AIDS on work productivity. In this paper, we consider the analysis of fractional-order mathematical models of the spread of HIV with productivity in the workplace. First, we estimate the epidemiological parameters of the HIV/AIDS model using the annual data of AIDS reported in Indonesia from 2006 to 2018. Based on the model analysis, two equilibria are determined, namely the HIV disease-free and endemic equilibrium’s. The disease-free equilibrium of HIV is locally asymptotically stable if the basic reproduction number is less than one, while the endemic equilibrium is globally asymptotically stable if the reproduction number is greater than one. The sensitivity analysis and numerical simulations are then carried out with variations in fractional order values to determine the dynamics of HIV spread with on-site productivity. Based on numerical simulation results, it was found that the transition rate of HIV-productive workers to AIDS sufferers could reduce the labor population of people living with AIDS and increase the workforce population vulnerable to HIV infection.
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