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The application of mathematical biology and dynamical systems has proven to be an effective approach for studying viral infection models. To contribute to this research, our paper proposes a new CHIKV model that takes into account an adaptive immune response and distributed time delays, which accurately reflects the time lag between initial viral contacts and the production of new active CHIKV particles. By analyzing the model’s qualitative behavior, we establish a biological threshold number that can predict whether CHIKV will be cleared from or persist in the body. We demonstrate the global stability of both CHIKV-present and CHIKV-free steady states using the Lyapunov functional method and LaSalle’s invariance principle. In addition, we conduct numerical simulations to examine how time delays can affect the stability of the steady states. Through these simulations, we gain insights into how varying time delays can influence the persistence or clearance of CHIKV within the host. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear model is proposed and analyzed to study the spread of Leukemia by considering the effect of genetically engineered patients T cells to attack cancer cells. The model is governed by four dependent variables namely; naive or susceptible blood cells, infected or dysfunctional blood cells, cancer cells and immune cells. The model is analyzed by using the stability theory of differential equations and numerical simulation. We have observed that the system is stable in the local and global sense if antigenicity rate or rate of stimulation of immune cells is greater than a threshold value dependent on the density of immune cells. Further, external infusion of T cells (immune cells) reduces the concentration of cancer cells and infected cells in the blood. It is observed that the infected cells decrease with the increase in antigenicity rate or stimulation rate of immune response due to abnormal cancer cells present in the blood. This indicates that immune cells kill cancer cells on being stimulated and as antigenicity rate increases rate of destruction of cancer cells also increase leading to decrease in the concentration of cancer cells in the body. This decrease in cancer cells further causes decrease in the concentration of infected or dysfunctional cells in the body. [ABSTRACT FROM AUTHOR]

We consider a mathematical model that describes a viral infection of HIV-1 with both virus-tocell and cell-to-cell transmission, CTL response immune and four distributed delays, describing intracellular delays and immune response delay. One of the main features of the model is that it includes a constant production rate of CTLs export from thymus, and an immune response delay. We derive the basic reproduction number and show that if the basic reproduction number is less than one, then the infection free equilibrium is globally asymptotically stable; whereas, if the basic reproduction number is greater than one, then there exist a chronic infection equilibrium, which is globally asymptotically stable in absence of immune response delay. Furthermore, for the special case with only immune response delay, we determine some conditions for stability switches of the chronic infection equilibrium. Numerical simulations indicate that the intracellular delays and immune response delay can stabilize and/or destabilize the chronic infection equilibrium. [ABSTRACT FROM AUTHOR]

We present the dynamical behaviors of a virus infection model with general infection rate, immune responses and two intracellular delays which describe the interactions of the HIV virus, target cells, CTL cells and antibodies within host. Three factors are incorporated in this model: (1) the intrinsic growth rate of uninfected cells, (2) a nonlinear incidence rate function considering both virus-tocell infection and cell-to-cell transmission, and (3) a nonlinear productivity and removal function. By the method of Lyapunov functionals and LaSalle's invariance principle, we show that the global dynamics of the model is determined by the reproductive numbers for viral infection R0, for antibody immune response R1, for CTL immune response R2, for CTL immune competition R3 and for antibody immune competition R4. The numerical simulations are given to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]