CRITICAL CONTACT RATE FOR VECTOR–HOST–PATHOGEN OSCILLATION INVOLVING CO-FEEDING AND DIAPAUSE

Abstract

We consider the dynamic vector–host–pathogen interaction motivated by tick-borne diseases such as tick-borne encephalitis and Lyme disease. We stratify the vector population in terms of the stage before and after the vector’s contact with hosts when co-feeding transmission may take place, and we also consider the case where vector development may involve two time lags due to normal development and diapause. We derive threshold conditions for disease persistence and for nonlinear oscillations in the vector population and in the diseased vector and host populations. Our objective here is to use a simple mechanistic dynamic model to show that diapause and co-feeding transmission may generate periodic and irregular oscillations even when seasonal variations of the environmental conditions are ignored. These oscillations are not necessary in synchrony with the seasonality of vector development, and hence complicated oscillatory patterns of vector-borne disease dynamics in the field and surveillance observations should be expected.