Modeling within-host Chikungunya virus dynamics with the immune system using semi-analytical approaches.

Objective: Chikungunya fever continues to spread worldwide due to its asymptomatic nature and lack of a specific treatment. A mathematical model using the Caputo fractional order derivative is developed to study the interactions between host defense cells and Chikungunya viral particles in this research. The model's solution existence, uniqueness, and positivity are analyzed. The disease-free state threshold and Hyers-Ulam stability are established.

Results: The basic reproductive number $R_0\approx 7$ , depict a high replication rate of the virus, indicating an increased infectiousness of uninfected cells. Sensitivity analysis shows that the invasion rate of susceptible monocytes increases spread, while antigenic immune response keeps $R_0$ below 1. The Laplace Adomian Decomposition Method (LADM) is used to solve the model. Experimental outcomes suggest that the enhanced adaptive immune response, potentially influenced by nutritional support or medication, exhibits a more pronounced hysteresis effect. We observed that viral particles are cleared approximately three (3) days earlier before cell infection, potentially clearing the virus within a week. This insight could accelerate elimination of viral particles and expedite virus clearance.