The dynamics of simultaneous infections with altered susceptibilities

We describe a model in which individuals can be infected simultaneously by multiple diseases or parasites, taking into account the fact that individuals already infected by a subset of n co-circulating diseases may see their susceptibility to concurrent infection by another disease from the pool either enhanced or reduced. We propose an n-dimensional approximation to the 2n dimensional model required to describe the dynamics of each possible subset of the pool of n co-circulating diseases, using as state variables the overall prevalence of each infection. Analysis of the two disease case shows that the reduced model provides a very good approximation throughout the full dynamics for small alterations of susceptibility, and, after a transient error, a good approximation to the complete model when susceptibilities are highly enhanced. As the number of diseases becomes large, the approximation remains close for small alterations of susceptibility.