Application of piecewise mathematical modeling to analyse the effect of HIV/AIDS on working class: The case of Ethiopia

Abstract

In this study, we employed a novel combination of piecewise models to investigate the impact of IV/AIDS on the working class in Ethiopia. The piecewise model was changed from deterministic to stochastic, from fractal-fractional to a random, and from deterministic to fractal-fractional, then to stochastic. This innovative piecewise model takes into account data fitting for working-class HIV/AIDS cases for the period 2000–2022. According to numerical simulation, fractional model-follow stochastic models are more reliable than deterministic model-follow stochastic models. Numerical simulations show that decreasing the contact rate decreases the number of individuals infected with HIV/AIDS infection, decreasing the contact rate to eradicate HIV/AIDS infection before the estimated time, and increasing the contact rate prolongs the estimated time to end HIV/AIDS infection. According to the numerical simulation result, non-productivity increases the chance of being infected by HIV/AIDS. As the rate at which non-productive classes become productive increases, the productivity force of the population increases, and the non-productive class of the population decreases. This condition is used to quickly eradicate HIV/AIDS infection by decreasing the inequality due to the economic crisis.