Modelling heterogeneous host immune response in a multi-strain system

We explore the dynamics that occur when multiple variants of a virus are released in a population, where hosts can make an immune response to only one epitope of the virus. A heterogeneous immune response was implemented by varying the probability for making a response at a locus of the virus variants. A framework based on an SIR model is presented which allows for the explicit representation of the virus variants and the immune histories of the population. From this we are able to calculate the proportion of the population infected by each variant and the number of times a host has been infected when there have been multiple epidemics. When there are discrete epidemics, we use the framework to calculate the proportion of the population infected analytically, demonstrating a method which reduces the calculations required in comparison with solving the full system of differential equations. However, when there are multiple strains present in the population at any time, we show that the full set of ODEs must be solved to fully describe the infection dynamics.