dynamics analysis of a hiv infection model with the effect release of inflammatory cytokines

Hiv disease is a type of chronic disease that over time causes a decrease inthe body’s immune system cells, especially t cells. one of the main questions aboutthis disease is that t cells depletion can take many years but slow decline are not wellunderstood. in some studies they showed that infected t cells die in the lymph nodes bya type of cell death called pyroptosis cell death. in this type of cell death, inflammatorycytokines can be released, thus attracting more t cells. in this paper, a model for hivinfection with the effect release of inflammatory cytokines on interaction between thet cells and virus is considered. this model includes the dynamic behavior of the uninfected and infected t cell, and the hiv viral load. in this model, the proliferation of tcells is a logistic growth and the infection function of t cells is beddington–deangelisfunction. we prove that if the basic reproduction number is less than one then theinfection free equilibrium point of the model is globally asymptotically stable and ifmore than one, then the endemic infection equilibrium point of the model is globallyasymptotically stable. in the end, we showed the existence of the condition by creatingan orbitally asymptotically stable periodic solution numerical results.