In-host fractional order model for malaria parasite dynamics with immune system

A cell-level dynamical model accounting for memory effects and human host defense is critical in many aspects of the disease, particularly in the vector-mediated transmission from human to human in the community and in designing effective intervention strategies. In this work, a fractional order model for malaria parasite infection within the human host is formulated and analyzed. The presented model aims to investigate the dynamical behavior of in-host malaria infection with memory effect by considering populations of liver hepatocyte cells, red blood cells, and malaria parasites in the presence of the immune system. The model is governed by an eight-dimensional system of differential equations with immunological responses. We examine the basic properties of the model, like the existence, uniqueness, boundedness, and non-negativity of the solution, using well-established mathematical theories. Then, we perform the analysis by describing the expression for the basic reproduction ratio, \(R_{0}\) $R_0$ . We found that the parasite-free steady state is locally asymptotically stable if \(R_{0}<1\) $R_0<1$ . Otherwise, if \(R_{0}>1\) $R_0>1$ , it is violated and the parasite persistent steady state exists. Sensitivity analysis of the basic reproduction ratio reveals that the infection rate of erythrocytes, the average number of merozoites per bursting blood schizont, and the requirement rate of erythrocytes are the most influential parameters. Finally, to validate our theoretical findings, various numerical simulations are presented using the generalized predictor-corrector of the Adams-Bashforth-Moulton method. The simulation results suggested that an average number of merozoites per rupturing infected hepatocyte and infected erythrocyte and the inhibition rate of the invasion of uninfected hepatocytes and erythrocytes have a high effect on the within-host dynamics of the parasite.