Periodic solutions in an SIRWS model with immune boosting and cross-immunity

Abstract

Incidence of whooping cough, an infection caused by Bordetella pertussis and Bordetella parapertussis, has been on the rise since the 1980s in many countries. Immunological interactions, such as immune boosting and cross-immunity between pathogens, have been hypothesised to be important drivers of epidemiological dynamics. We present a two-pathogen model of transmission which examines how immune boosting and cross-immunity can influence the timing and severity of epidemics. We use a combination of numerical simulations and bifurcation techniques to study the dynamical properties of the system, particularly the conditions under which stable periodic solutions are present. We derive analytic e..