A mathematical model for varicella-zoster and HIV co-dynamic supported by numerical simulations

The prevalence of the varicella-zoster virus (VZV) and its correlation underscore its impact on a significant segment of the population. Notably contagious, VZV serves as a risk factor for the manifestation of HIV/AIDS, with its reactivation often signaling the onset of immunodeficiency. Recognizing the concurrent existence of these two diseases, this study focuses on the co-infection dynamics through a deterministic mathematical model. The population is categorized into seven exclusive groups, considering the complexities arising from the interplay of HIV and Zoster. We establish the non-negativity and boundedness of solutions, examine equilibrium points, calculate basic reproduction numbers via the next-generation matrix approach, and analyze the existence and local stabilities of equilibriums using the Routh-Hurwitz stability criteria. The numerical simulations reveal that the model converges to an endemic equilibrium point when the reproduction number exceeds unity. The primary objectives of this study are to comprehensively understand the transmission dynamics of HIV and Zoster in a co-infected population and to provide valuable insights for developing effective intervention strategies. The findings emphasize the importance of addressing these co-infections to mitigate their impact on public health.