Effect of cross-immunity in a two-strain cholera model with aquatic component

The bacteria Vibrio cholerae relies heavily upon an aquatic reservoir as a transmission route with two distinct serotypes observed in many recent outbreaks. In this paper, we extend previously studied ordinary differential equation epidemiological models to create a two-strain SIRP (susceptible-infectious-recovered-pathogen) system which incorporates both partial cross-immunity between disease strains and environmental pathogen transmission. Of particular interest are undamped anti-phase periodic solutions, as these display a type of coexistence where strains routinely switch dominance, and understanding what drives this switch can optimize the efficiency of the host population's control measures against the disease. We derive the basic reproduction number R-0 and use stability analysis to examine the disease free and single-strain equilibria. We formulate a unique coexistence equilibrium and prove uniform persistence of both strains when R-0>1. In addition, we simulate solutions to this system, along with seasonally forced versions of the model with and without host coinfection. Cross-immunity and transmission pathways influence damped or sustained oscillatory dynamics, where the presence of seasonality can modify, amplify or synchronize the period and phase of serotypes, driving epidemic waves. Cycling of serotypes over large time intervals, similar to observed data, is found for a range of cross-immunity levels, and the inclusion of coinfection in the model contributes to sustained anti-phase periodic solutions.

Automated summary

In this study, the researchers extended previous epidemiological models to incorporate partial cross-immunity and environmental pathogen transmission in a two-strain SIRP system. They focused on undamped anti-phase periodic solutions and derived the basic reproduction number R-0. They found that cross-immunity and transmission pathways influenced the dynamics of the disease and that the presence of seasonality modified the period and phase of the serotypes, driving epidemic waves.