Abstract:
:In this paper, a simple semi-discrete (ticks' feeding is assumed to occur only during the 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.
journal_name
Bull Math Bioljournal_title
Bulletin of mathematical biologyauthors
Ghosh M,Pugliese Adoi
10.1016/j.bulm.2004.03.007subject
Has Abstractpub_date
2004-11-01 00:00:00pages
1659-84issue
6eissn
0092-8240issn
1522-9602pii
S0092824004000412journal_volume
66pub_type
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