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.
Highlights
We consider the transmission dynamics of tick-borne diseases such as tick-borne encecphalitis and Lyme disease
Tick-borne diseases can be caused by infection
In Europe and Asia, Ixodes ricinus and Ixodes persulcatus ticks are primary species transmitting tick-borne encephalitis and Lyme borreliosis, infections can be transmitted through ingesting contaminated unpasteurized cow, sheep or goat milk and milk products obtained from infected animals
Summary
We consider the transmission dynamics of tick-borne diseases such as tick-borne encecphalitis and Lyme disease. Dunn et al.[7] performed a global sensitivity analysis to rank the importance of model parameters in terms of their contribution to the observed variations in the basic reproduction number They concluded that there are three most influential factors: the transmission efficiency from the vertebrate host to ticks, the survival rate from fed larva to feeding nymph, and the fraction of nymphs finding a competent host. Lou et al.[8] proposed a stage-structured periodic model to identify the tick reproduction threshold and the disease spread threshold, and investigated effects of seasonal temperature variation and host community composition on the pattern of Lyme disease spread. None of these models have incorporated the roles of co-feeding transmission and diapause. A natural question is whether such a model can exhibit nonlinear oscillations
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