Disease induced oscillations between two competing species

The interaction of disease and competition dynamics is investigated in a system of two competing species in which only one species is susceptible to disease. The model is kept as simple as possible, combining Lotka-Volterra competition between the species with disease dynamics of susceptible and infective individuals within one of the species. It is assumed that pure vertical disease transmission ( from parent to offspring) dominates horizontal transmission ( by contact between infective and susceptible individuals) and that infective individuals have the same competition strength as susceptibles but a lower intrinsic growth rate. These assumptions yield three-dimensional competitive Lotka-Volterra dynamics modeling the disease-competition interaction. It is proved that if in the absence of disease there is competitive exclusion between the two species, then the presence of disease can lead to stable or oscillatory coexistence of both species. The case of oscillatory coexistence can be viewed either as disease induced oscillations between competing species or as competition induced oscillations in an endemic disease. By contrast, conditions are found under which, if the two species coexist in the absence of disease, then the introduction of disease does not induce oscillations, and the long-term dynamics are determined by the basic reproduction number.