Comprehensive analysis of mathematical model of HIV/AIDS incorporating fisher-folk community

The Human Immunodeficiency Virus (HIV) is a pathogen that specifically targets the human immune system, leading to a more advanced condition known as acquired immunodeficiency syndrome (AIDS) when it significantly compromises the body’s immune defences. In this research, a comprehensive mathematical model for HIV/AIDS has been developed, encompassing the dynamics within both the general population and the fisher-folk population. Utilizing the next-generation matrix method, we calculate the basic reproduction number ( \({R}_{0}\) $R_0$ ), a crucial metric that quantifies the rate of HIV transmission. Through bifurcation analysis, we have explored the implications of varying \({\eta }^{*}\) $\eta _{}^{\ast }$ and \({\eta }_{F}^{*}\) $\eta _F^{\ast }$ , serving as bifurcation parameters, at the critical threshold where \({R}_{0}=1\) $R_0=1$ . A sensitivity analysis of the basic reproduction number \({R}_{0}\) $R_0$ is conducted for both the general community and the fisherfolk community. For the general community, the sensitivity parameters are \(\eta\) $\eta$ , \({\omega }_{F}\) ${\omega }_F$ , \(\phi\) $\varphi$ , and \({\eta }_{F}\) ${\eta }_F$ . For the fisher-folk community, the sensitivity parameters are \(\eta\) $\eta$ , \(\omega\) $\omega$ , \({\phi }_{F}\) ${\varphi }_F$ , and \({\eta }_{F}\) ${\eta }_F$ . This analysis enhances our understanding of the factors influencing HIV transmission rates. Using the Routh-Hurwitz criterion and Castillo Chavez's approach, we have demonstrated the HIV-free equilibrium is locally asymptotically stable and globally asymptotically stable when \({R}_{0}<1\) $R_0<1$ , respectively. Furthermore, the research explores the graphical behavior of both the general and fisher-folk communities, providing insights into their respective dynamics.