Modeling the impact of host resistance on structured tick population dynamics

Mahnaz Alavinejad,Jianhong Wu,Jemisa Sadiku

doi:10.5206/mase/10508

Mahnaz Alavinejad, Jianhong Wu + Show 1 more

Open Access

https://doi.org/10.5206/mase/10508

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Abstract

For a variety of tick species, the resistance, behavioural and immunological response of hosts has been reported in the biological literature but its impact on tick population dynamics has not been mathematically formulated and analyzed using dynamical models reflecting the full biological stages of ticks. Here we develop and simulate a delay differential equation model, with a particular focus on resistance resulting in grooming behaviour. We calculate the basic reproduction number using the spectral analysis of delay differential equations with positive feedback, and establish the existence and uniqueness of a positive equilibrium when the basic reproduction number exceeds unit. We also conduct numerical and sensitivity analysis about the dependence of this positive equilibrium on the the parameter relevant to grooming behaviour. We numerically obtain the relationship between grooming behaviour and equilibrium value at different stages.

Highlights

Lyme Disease is the most reported athropod-borne illness and it was first recognized in 1976 in Lyme, Connecticut USA [22]
Borrelia burgdorferi is a tick-borne spirochete responsible for Lyme disease which is found in nymphal Ixodes dammini and has the highest chance to be transmitted to the host if the infected tick feeds for a duration of 72 hours or more [16, 23, 10]
Jennings et al [9] studied the effect of host resistance on tick population dynamics

Summary

Introduction

Lyme Disease is the most reported athropod-borne illness and it was first recognized in 1976 in Lyme, Connecticut USA [22]. Jennings et al [9] studied the effect of host resistance on tick population dynamics They developed a mathematical model, described by a system of ordinary differential equations, focusing on tick-host interaction where the tick’s life cycle was divided into two main stages, adult and juvenile, and the host was subdivided into host with no immunity and host with immunity. Their focus is to show how immunity affects the extinction or persistence of tick dynamics. The sensitivity analysis demonstrates the dependence of the solutions on different parameters

The Model Formulation

Analyses

Numerical Simulations

Findings

Conclusion