Asymptotic theory of an infectious disease model.
In this paper, we present asymptotic theory as a viable alternative solution method for infectious disease models. We consider a particular model of a pathogen attacking a host whose immune system responds defensively, that has been studied previously [Mohtashemi and Levins in J. Math. Biol. 43: 446-470 (2001)]. On rendering this model dimensionless, we can reduce the number of parameters to two and note that one of them has a large value that suggests an asymptotic analysis. On doing this analysis, we obtain a satisfying qualitative description of the dynamic evolution of each population, together with simple analytic expressions for their main features, from which we can compute accurate quantitative values.
Whitman
Alan M
AM
Department of Mechanical Engineering, Villanova University, 800 W. Lancaster Ave., Villanova, PA 19085, USA. alan.whitman@villanova.edu
Ashrafiuon
Hashem
H
D000465:Algorithms; D000818:Animals; D001419:Bacteria / Q000276:immunology*; D003141:Communicable Diseases / Q000276:immunology* / Q000382:microbiology / Q000821:virology; D006801:Humans; D018448:Models, Immunological; D014780:Viruses / Q000276:immunology*