HIV/AIDS control owing to local and global awareness, diagnosis, treatment tactics and control theory: fractional order modeling

Since there is no available vaccination for a contagious disease like HIV/AIDS, utilizing fractional order modeling in awareness, diagnosis, treatment, and control theory can be an effective method to prevent the spread of the disease. Consequently, we developed a novel mathematical model within a Caputo fractional framework to analyze the patterns of HIV/AIDS disease transmission. To make the unaware susceptibles aware, media-based global awareness and word-of-mouth communication based local awareness, together with psychological anxiety about infection among these conscious susceptibles, are incorporated here. Diagnosis process is taken into account to diagnosis the asymptomatic individuals to identify the AIDS and HIV symptomatic population. The local awareness and diagnosis rates are assumed dynamic, which are proportional to the aware, infectious and population under treatment. Taking advantage of the generalized mean value theorem, we first ensure the positivity, then applying the Mittag-Leffler function’s property, we show the biologically feasible region, and finally the solution’s existence and uniqueness are given by utilizing the Banach fixed point theorem. We present only local stability around the disease-free equilibrium point. Next local and global stabilities around the disease persistent equilibrium point-based are exhibited using the basic reproduction number ( \(R_0\) $R_0$ ). The direction of transcritical bifurcation is illustrated analytically using the unit epidemic edge. In order to identify the most important parameter(s) for our defined epidemic model, which are embedded in \(R_0\) $R_0$ , a quantitative assessment is conducted on \(R_0\) $R_0$ . To achieve the population dynamics’s trends, a numerical experiment is conducted here. During and after transition phases, we impose a strive for understanding the behavior of the order and kernel of the fractional derivative on the system’s dynamics and in the prevention of disease transmission. Based on the fractional optimal control theory, it is demonstrated that HIV/AIDS can be mathematically eradicated with the intervention strategies, namely, enhanced awareness, diagnosis and treatment. Fractional derivatives serve a crucial role in preventing the propagation of the disease and have a significant impact on the system’s dynamics during the transition period.