An evolutionary epidemiological mechanism, with applications to type A influenza

In this paper I develop a model that describes an evolutionary epidemiological mechanism and apply this model to the epidemiology of type A influenza. This evolutionary epidemiological model differs from the classical nonevolutionary epidemiological model which has been applied to diseases like measles, rubella, and whooping cough in having a novel mechanism which causes susceptible individuals to be introduced into the host population. In the nonevolutionary model, susceptibles are continually introduced into the host population by demographic processes: most hosts that die are immune, while newborn hosts are susceptible. In this evolutionary model, the susceptible class is continually replenished because the pathogen changes genetically, and hence immunologically, from one epidemic to the next, causing previously immune hosts to become susceptible. I derive formulae which describe how the equilibrium number of infected hosts, the interepidemic period, and the probability that a host will become reinfected depend on the rate of amino acid substitution in the pathogen, m, a parameter describing the effect of these substitutions on host immunity, gamma, as well as the host population size, N, and the recovery rate, r. To apply the model to influenza, I show how the nondimensional parameter epsilon = m gamma N/r2 may be estimated from four types of data. The methods are applied to several data sets, and I conclude that epsilon much less than 1; sampling variation and inconsistencies between the various data sets do not permit epsilon to be estimated more precisely. The evolutionary epidemiological model has no threshold host population size, in contrast to the nonevolutionary model.