Seasonal Population Dynamics of Ticks, and its Influence on Infection Transmission: A Semi-discrete Approach

Ghosh, Mini and Pugliese, Andrea (2003) Seasonal Population Dynamics of Ticks, and its Influence on Infection Transmission: A Semi-discrete Approach. UNSPECIFIED. (Unpublished)

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    Abstract

    In this paper, a simple semi-discrete (ticks’ feeding is assumed to occur only during summers of each year) model for tick population dynamics is presented. Conditions for existence, uniqueness, and stability of a positive equilibrium are found; the system is then studied numerically using parameter estimates calibrated for the tick Ixodes ricinus in Trentino, Italy, and the sensitivity to parameters is examined. Then, this model is extended to consider a tick-transmitted infection of one species of hosts, while other hosts are incompetent to the infection. Assuming, for simplicity, that the infection is not affecting the total number either of hosts or ticks, a threshold condition for infection persistence is obtained. The dependence of the equilibrium infection prevalence on parameters is studied numerically; in particular, we considered how infection prevalence depends on host densities. This analysis reveals that a ‘dilution effect’ occurs both for competent and for incompetent hosts; this means that, besides a lower threshold for host densities for infection to persist, there exists also an upper threshold: if host densities were higher than the upper threshold, the infection would go to extinction. Numerically, it is found that, for realistic parameter values, the upper threshold is not much higher than observed densities.

    Item Type: Departmental Technical Report
    Department or Research center: Mathematics
    Subjects: Q Science > QA Mathematics > QA276 Mathematical Statistics
    Uncontrolled Keywords: Tick-borne infections, semi discrete model, simulation, dilution
    Report Number: UTM 653, October 2003
    Repository staff approval on: 18 May 2005

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