Infestation Dynamics and Tick-on-Host Distribution Pattern Formation

Abstract

Through a co-feeding transmission route, a susceptible vector can acquire the infection by co-feeding with infected vectors on the same host even when the pathogen has not been established within the host for systemic transmission. As co-feeding depends on local infection rather the widespread pathogen within the host, the vector aggregation patterns on hosts are important for the effectiveness of co-feeding transmission. Modelling how these patterns are formed from the interactive vector attaching and host grooming behaviors, and understanding how the infestation dynamics influences and interacts with tick population dynamics and pathogen transmission dynamics is a topics of current interest. We start with a simple model with tick populations stratified in two different stages (larva and nymph) involved in the co-feeding transmission from infected nymphal ticks to susceptible larval ticks through a bridging host, and assuming co-feeding transmission is only possible when the tick loads are sufficient high. We then consider a more realistic situation that occurrence of co-feeding depends on the number of infected ticks feeding on a host, and we develop a delay vector-host population dynamics model incorporating vector attaching and host grooming behaviours. We introduce the concept of basic infestation number and use this number and other qualitative measures to characterize the distribution patterns. We provide some numerical examples to show how some of the derived tick-on-host distribution patterns lead to bi-stability and nonlinear oscillation in the vector and host populations.