Eﬀects of tick population dynamics and host densities
on the persistence of tick-borne infections
, Andrea Pugliese
Centre for Alpine Ecology, Viote del Monte Bondone, 38040 Trento, Italy
Department of Mathematics, University of Trento, Povo (TN), Italy
Received 29 November 2005; received in revised form 1 September 2006; accepted 11 October 2006
Available online 19 October 2006
The transmission and the persistence of tick-borne infections are strongly inﬂuenced by the densities and
the structure of host populations. By extending previous models and analysis, in this paper we analyse how
the persistence of ticks and pathogens, is aﬀected by the dynamics of tick populations, and by their host
densities. The eﬀect of host densities on infection persistence is explored through the analysis and simula-
tion of a series of models that include diﬀerent assumptions on tick–host dynamics and consider diﬀerent
routes of infection transmission. Ticks are assumed to feed on two types of host species which vary in their
reservoir competence. Too low densities of competent hosts (i.e., hosts where transmission can occur) do
not sustain the infection cycle, while too high densities of incompetent hosts may dilute the competent hosts
so much to make infection persistence impossible. A dilution eﬀect may occur also for competent hosts as a
consequence of reduced tick to host ratio; this is possible only if the regulation of tick populations is such
that tick density does not increase linearly with host densities.
Ó 2006 Elsevier Inc. All rights reserved.
Keywords: Tick-borne infections; Tick population dynamics; Basic reproduction number; Host density; Dilution eﬀect
0025-5564/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved.
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Mathematical Biosciences 208 (2007) 216–240