Delay differential systems for tick population dynamics.
J Math Biol
; 71(5): 1017-48, 2015 Nov.
Article
em En
| MEDLINE
| ID: mdl-25348048
ABSTRACT
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 [Formula see text] of stage structured tick populations. The tick population is uniformly persistent if [Formula see text] and dies out if [Formula see text]. 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.
Palavras-chave
Texto completo:
1
Coleções:
01-internacional
Base de dados:
MEDLINE
Assunto principal:
Carrapatos
/
Modelos Biológicos
Tipo de estudo:
Prognostic_studies
Limite:
Animals
/
Female
/
Humans
/
Male
Idioma:
En
Revista:
J Math Biol
Ano de publicação:
2015
Tipo de documento:
Article
País de afiliação:
Estados Unidos