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An age-structured mathematical model for the within host dynamics of malaria and the immune system. (English) Zbl 1132.92016
Summary: We use a mathematical model to study the population dynamics of replicating malaria parasites and their interaction with the immune cells within a human host. The model is formulated as a system of age-structured partial differential equations that are integrated over age to obtain a system of nonlinear delay differential equations. Our model incorporates an intracellular time delay between the infection of the red blood cells by the merozoites that grow and replicate within the infected cells to produce new merozoites. The infected red blood cells burst approximately every 48 h releasing daughter parasites to renew the cycle. The dynamical processes of the parasites within the human host are subjected to pressures exerted by the human immunological responses. The system is then solved using a first-order, finite difference method to give a discrete system. Numerical simulations carried out to illustrate stability of the system reveal that the populations undergo damped oscillations that stabilise to steady states.

MSC:
92C60 Medical epidemiology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
65N06 Finite difference methods for boundary value problems involving PDEs
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