Analysis of periodic solutions in an eco-epidemiological model with saturation incidence and latency delay

被引:11
|
作者
Bhattacharyya, R. [2 ]
Mukhopadhyay, B. [1 ]
机构
[1] Cent Calcutta Polytech, Dept Sci, Kolkata 700014, India
[2] Calcutta Tech Sch, Dept Sci, Kolkata 700013, India
关键词
Saturation incidence; Latency delay; Periodic solution; Supercritical Hopf bifurcation; Subcritical Hopf bifurcation; PREDATOR-PREY MODEL; PARASITE POPULATION INTERACTIONS; NONLINEAR INCIDENCE RATES; INFECTIOUS-DISEASES; SALTON-SEA; BEHAVIOR; STABILITY; PELICANS; SYSTEMS; RISK;
D O I
10.1016/j.nahs.2009.09.007
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In the present work, a mathematical model of predator-prey ecological interaction with infected prey is investigated. A saturation incidence function is used to model the behavioral change of the susceptible individuals when their number increases or due to the crowding effect of the infected individuals [V. Capasso, G. Serio, A generalization of the Kermack-McKendrick deterministic epidemic model, Math. Biosci. 42 (1978) 41-61]. Stability criteria for the infection-free and the endemic equilibria are deduced in terms of system parameters. The basic model is then modified to incorporate a time delay, describing a latency period. Stability and bifurcation analysis of the resulting delay differential equation model is carried out and ranges of the delay inducing stability and as well as instability for the system are found. Finally, a stability analysis of the bifurcating solutions is performed and the criteria for subcritical and supercritical Hopf bifurcation derived. The existence of a delay interval that preserves the stability of periodic orbits is demonstrated. The analysis emphasizes the importance of differential predation and a latency period in controlling disease dynamics. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码:176 / 188
页数:13
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