During the process of immune response to the infection caused by dengue virus, antibodies are generated by plasma cells which are produced by B-cells. In some cases, it is observed that there is a delay in the production of plasma cells from B-cells which causes a delay in the immune response. We propose a SIVA within-host model of the virus transmission with delayed immune response to articulate the dynamics of the cell and virus population. The stability analysis of different equilibrium states is also studied. The basic reproduction number (BRN) of the model is computed using next generation matrix (NGM) method. The local stability analysis is discussed using the method of linearisation. The stability conditions of the equilibrium states are validated using the Li´enard - Chipart criterion. Hopf bifurcation analysis is carried out as the system has time lag in the immune response. Three equilibrium states, namely, virus free equilibrium state, endemic equilibrium state with and without immune response, have been observed. It has been found that the virus free equilibrium state is locally asymptotically stable if BRN is less than or equal to 1. Additionally, the conditions for the stability of the endemic equilibrium points are derived and elaborated. Numerical simulations for different values of time delay parameter τ are presented and illustrated using graphs. A Hopf bifurcation is observed if the delay parameter τ crosses a threshold value and then the system becomes unstable with periodic solution. To determine the relative importance of the model parameters to the virus transmission and prevalence, sensitivity analysis of the parameters is illustrated using graphs. Due to the time lag in the immune response, an increase in the virus growth is observed in large quantity. As a result, the infection spreads more quickly within the host.

Dengue fever is an infectious viral fever. The complex behavior of the virus within the body can be explained through mathematical models to understand the virus’s dynamics. We propose two different with-in host models of dengue virus transmission with humoral immune response. The proposed models differ from one another because one of the models assumes that newly formed viruses infect healthy cells again. To understand the dynamics of the proposed models, we perform a comparative study of stability analysis, numerical simulation, and sensitivity analysis. The basic reproduction number (BRN) of the two models is computed using next-generation matrix method. The local stability (l.s) analysis is discussed using the linearization method. The Lyapunov’s direct method is used to check the global stability (g.s) of the models. It has been found that both the equilibrium states for both the models, namely, virus-free equilibrium state and endemic equilibrium state, are globally stable, based on the value of BRN. Results show the influence of immune response on the cell dynamics and virus particles. The virus neutralization rate by antibodies and rate that affects the antibody growth are highly sensitive for the two models. Optimal control is applied to explore the possible control strategies to prevent virus spread in the host system. It is evident from the results that the strategy to administrate antibiotic drugs and home remedies slow down the virus spread in the host.

No abstract