Delay differential systems for tick population dynamics

被引:25
作者
Fan, Guihong [1 ]
Thieme, Horst R. [2 ]
Zhu, Huaiping [3 ]
机构
[1] Columbus State Univ, Dept Math & Philosophy, Columbus, GA 31907 USA
[2] Arizona State Univ, Sch Math & Stat Sci, Tempe, AZ 85287 USA
[3] York Univ, Dept Math & Stat, Toronto, ON M3J 2R7, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
Tick populations; Stage structure; Delay differential systems; Local stability; Global stability; Persistence; Basic reproduction number; Integral equations; INFECTION TRANSMISSION; MODEL; PERSISTENCE; SEASONALITY; VECTOR; NUMBER;
D O I
10.1007/s00285-014-0845-0
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
Ticks play a critical role as vectors in the transmission and spread of Lyme disease, an emerging infectious disease which can cause severe illness in humans or animals. To understand the transmission dynamics of Lyme disease and other tick-borne diseases, it is necessary to investigate the population dynamics of ticks. Here, we formulate a system of delay differential equations which models the stage structure of the tick population. Temperature can alter the length of time delays in each developmental stage, and so the time delays can vary geographically (and seasonally which we do not consider). We define the basic reproduction number of stage structured tick populations. The tick population is uniformly persistent if and dies out if . We present sufficient conditions under which the unique positive equilibrium point is globally asymptotically stable. In general, the positive equilibrium can be unstable and the system show oscillatory behavior. These oscillations are primarily due to negative feedback within the tick system, but can be enhanced by the time delays of the different developmental stages.
引用
收藏
页码:1017 / 1048
页数:32
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