An age-structured mathematical model for the within host dynamics of malaria and the immune system
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Date
2007
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract
In the paper, 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 then 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.
Description
Keywords
Age-structured, Immune system, Parasite replication, Time delay
Citation
Tumwiine, J., Luckhaus, S., Mugisha, J. Y. T., & Luboobi, L. S. (2008). An age-structured mathematical model for the within host dynamics of malaria and the immune system. Journal of Mathematical Modelling and Algorithms, 7, 79-97.doi:10.1007/s10852-007-9075-4