A fractional-order nonlinear model for a within-host chikungunya virus dynamics with adaptive immunity using Caputo derivative operator

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The study of within-host dynamics of viral infection is a vital process of understanding how healthy cells in the body are affected by viral foreign bodies and how body immunity responds to such changes. This paper presents and analyses the dynamics of a within-host Chikungunya virus transmission with adaptive immune responses using a fractional-order derivative operator of the Caputo type. The formulated model describes the interaction of uninfected cells, infected cells and viral particles in the presence of Cytotoxic T-Lymphocytes and antibody immune responses. Several analytical methods are employed to analyse the fractional-order within-host model. Positivity and boundedness theory are used to investigate the properties of solutions of the model via the generalized mean value theorem approach. The existence and uniqueness of solutions are examined using the Banach fixed point method. The normalized forward sensitivity method determines how different model parameters affect the fractional-order system. It was shown that transmission rate and parameters representing adaptive immune responses played a significant role in the Chikungunya virus model’s dynamics. Further, the time-dependent optimal control fractional-order model is analysed to optimize the performance of adaptive immune responses using the optimal control theory approach made popular by Pontryagin’s maximum principle. Simulations are performed to visualize the theoretical results and show the influence of memory on the trajectories of concentrations of uninfected cells, infected cells, viral particles, Cytotoxic T-Lymphocytes and antibodies.