Lenti-virus progression in a time-fractionality mathematical perspective

Abstract

The transmission of deadly virus are threatening the human evaluation, recent virus includes COVID-19, Monkey-pox and so on. But still the human evaluation is lacking to overcome the 18 century virus like lenti-virus which causes a primary infection called HIV-1 and HIV-2 to the human beings. In this paper, we discussed about the mathematical model in a time fractional Caputo derivative type for the transmission of this deadly virus. Our objective is to find out how control measures should be applied over a given time frame to minimize intervention costs while reducing the number of individuals that are afflicted right now. First the proposed models well-possedness is analyzed. Further, the transmission threshold called a basic reproduction number is obtained. Moreover, the sensitivity analysis are carried out to determine the effectiveness of the model parameter. The stability nature of the proposed model is discussed. Two control measures are included and the optimal control analysis are performed using the Pontryagin Maximum principle to control the disease spread in the environment. Finally all the theoretical findings are validated using the numerical simulation.