Analysis of the multistrain asymmetric SI model for arbitrary strain diversity

The asymmetric multistrain SI model is studied within a history-based framework. The governing differential equation in set notation is solved by making use of the powerful set manipulation functions of the Mathematica programming language. The algorithm allows, for the first time, the solution of both the temporal and the equilibrium equations for arbitrary strain diversity. Since Mathematica is an algebraic manipulator, analytical expressions are presented for the equilibrium population variables in terms of the forces of infection for arbitrary number of strains, n. Since there are no recoveries allowed in this model, it is found that coinfection always dominates the system if the basic reproductive number of both strains is greater than 1. The danger of coinfection is already evident for the relatively simple case of n=2 and becomes more drastic as n increases. Strains which are not sustainable on their own are prevalent in the host population due to coinfection. The notion of a prevalence distribution function is introduced, which shows how the total prevalence is distributed amongst the different levels of infection. Results indicate that higher values of n lead to a faster increase in coinfection prevalences since there are no recoveries in the model.