An epidemic model with host cross-immunity to a continuum of strains.
by
Farida Chamchod
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
Coauthors: Nicholas F Britton

Several models in multi-strain diseases have included cross-immunity. Lots of them are

complicated to deal with when the number n of strains increases. A history-based model for

example contains 2^n+n*2^(n-1) variables. However, in a status-based model the number of

variables is 2^n+n-1 and by the reduced-transmission and polarized immunity assumptions the

numbers of variables in total is drastically reduced to 2n. In this work, the model is based

on the status-based formulation. We use a real line with each point representing a strain

with a particular antigenic make-up to represent a phylogeny of the diseases. The number of

equations is now 2. We then study a travelling wave of the system and how it depends on other

parameters such as the mutation rate, the basic reproductive ratio, and the cross-immunity

coefficient. From the result, we conclude that the travelling wave represents an antigenic

drift process with strains present in the population dying out and being replaced by new ones

at new points in the antigenic space.

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Date received: March 26, 2008