Interactions of Multiple Strain Pathogen Diseases in the Presence of Coinfection, Cross Immunity, and Arbitrary Strain Diversity

A model for coinfection in multiple strain infectious diseases is developed to incorporate coinfection statuses, immune and infection history, and cross immunity. It is solved for the symmetric interior equilibrium through the use of a ladder operator formalism inspired by quantum mechanical methods. We find that coinfection can fundamentally affects transmission dynamics with important epidemiologic and evolutionary consequences. It can significantly shift the distribution of age at infection for highly antigenically diverse pathogens so that in small host populations, an evolutionary strategy maximizing individual strain transmissibility might be less optimal than one which maximizes the total prevalence of all strains in the system. Alternatively, mechanisms which inhibit coinfection and thus increase total infection prevalence may be evolutionarily advantageous.

Figure 1

The total prevalence $y_T$ as a function of the cross-immunity parameter $\varphi$ with $\eta =1$, $e=0.3$, and $n=50$. The solid line represents the total prevalence with coinfection and no cross immunity, the dashed line the total prevalence with coinfection and cross immunity, and the long-dashed-short-dashed line the total prevalence with coinfection inhibition. Note that $\varphi =1$ imply no cross immunity while $\varphi =0$ imply total cross immunity.

Figure 2

The total prevalence in the presence of the two forms of cross immunity and coinfection as a function of the cross-immunity parameters $\varphi$ and $\eta$. For this calculation $n=50$, $R_0=4$ and $e=0.3$.

Figure 3

Individual versus total prevalence. The total ($y_T$) and individual ($y_1$) strain prevalences, in the presence ($\varphi =1$) and absence ($\varphi =0$) of coinfection, as a function of the reproductive number ($R_0$). Here $n=50$, $\eta =1$, and $e=0.1$.