Stability Analysis of Within Host Dengue Model Incorporating the Impact of Cell-Mediated and Innate Immune Reactions

Author: Kunwer Singh Mathur and Bhagwan Kumar

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Abstract

Dengue a globally prevalent mosquito-borne disease affects millions each year. Developing a model to understand its dynamics within hosts is crucial for effective prevention and control. Mathematical models considering vector-host interactions, innate immunity, and IFN levels shed light on the interplay between host defences and viral spread. This paper deals with the analysis of a within-host dengue infection model with innate and adaptive immunity. In this context, a nonlinear mathematical model is developed and analyzed to reveal the growth of infection within host along with innate and adaptive immunity. The model has two equilibria: infection-free and endemic equilibrium. The infection-free equilibrium is locally and globally stable for R0 < 1, while numerically it is found that endemic equilibrium is locally and globally asymptotically stable for R0 > 1. Further, all the analytical results are verified through numerical simulations using MATLAB.

Keywords

Dengue infection, Antibodies, Basic reproduction number, Innate immunity, T immune cells

Conclusion

In this paper, a non-linear dynamical model is proposed to analyze the dynamics of dengue infection within a host and to understand the effect of innate immune response in the form of type I interferon as well as adaptive immune response in the form of B cells, T helper cells, antibodies. We have studied the model analytically and numerically to capture the qualitative behaviour of virus dynamics within the host. The disease-free and endemic equilibria are obtained and studied, which depends upon a basic reproduction number 〖(R〗_0). The disease-free equilibrium point is locally and globally asymptotically stable when basic reproduction number R_0<1 and unstable when R_0>1. Based on numerical simulation, the endemic equilibrium point appears to be locally and globally stable. All analytical results were also verified through numerical simulations. Further, since the infected cells activate the immune system and its rate is inversely proportional to the basic reproduction number, the higher rate is more beneficial in killing the virus. Similarly, T cell activates the B cells and B cells, which further differentiates into plasma cells through antibodies. These plasma cells can kill the virus. Hence, the rate f to produce antibodies here is also inversely proportional to R_0, which depicts an adverse effect on the virus. Finally, it is concluded that the basic reproduction number is crucial for controlling disease outbreaks in the study of disease dynamics.

References

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How to cite this article

Kunwer Singh Mathur and Bhagwan Kumar (2023). Stability Analysis of Within Host Dengue Model Incorporating the Impact of Cell-Mediated and Innate Immune Reactions. Biological Forum – An International Journal, 15(6): 674-678.