Article

A delayed epidemic model with stage-structure and pulses for pest management strategy

Department of Mathematics, Jiangsu University, ZhenJiang, JiangSu 212013,PR China; Department of Applied Mathematics, Dalian University of Technology, DaLian, LiaoNing 116024, PR China; Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain
Nonlinear Analysis Real World Applications (Impact Factor: 2.2). 01/2008; DOI: 10.1016/j.nonrwa.2007.05.004

ABSTRACT From a biological pest management standpoint, epidemic diseases models have become important tools in control of pest populations. This paper deals with an impulsive delay epidemic disease model with stage-structure and a general form of the incidence rate concerning pest control strategy, in which the pest population is subdivided into three subgroups: pest eggs, susceptible pests, infectious pests that do not attack crops. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact periodic susceptible pest-eradication solution of the system and observe that the susceptible pest-eradication periodic solution is globally attractive, provided that the amount of infective pests released periodically is larger than some critical value. When the amount of infective pests released is less than another critical value, the system is shown to be permanent, which implies that the trivial susceptible pest-eradication solution loses its attractivity. Our results indicate that besides the release amount of infective pests, the incidence rate, time delay and impulsive period can have great effects on the dynamics of our system.

0 Bookmarks
 · 
76 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: A model for a generic disease with incubation and recovered stages is proposed. It incorporates a vaccinated subpopulation which presents a partial immunity to the disease. We study the stability, periodic solutions and impulsive vaccination design in the generalized modeled system for the dynamics and spreading of the disease under impulsive and non-impulsive vaccination. First, the effect of a regular impulsive vaccination on the evolution of the subpopulations is studied. Later a non-regular impulsive vaccination strategy is introduced based on an adaptive control law for the frequency and quantity of applied vaccines. We show the later strategy improves drastically the efficiency of the vaccines and reduce the infectious subpopulation more rapidly over time compared to a regular impulsive vaccination with constant values for both the frequency and vaccines quantity.
    Nonlinear Analysis: Modelling and Control 01/2014; 19(1):83-108. · 0.86 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, we propose and analyze an ecological system consisting of pest and its natural enemy as predator. Here we also consider the role of infection to the pest population and the presence of some alternative source of food to the predator population. We analyze the dynamics of this system in a systemic manner, study the dependence of the dynamics on some vital parameters and discuss the global behavior and controllability of the proposed system. The investigation also includes the use of pesticide control to the system and finally we use Pontryagin’s maximum principle to derive the optimal pest control strategy. We also illustrate some of the key findings using numerical simulations.
    Nonlinear Dynamics 11/2013; · 3.01 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: A SVEIR model with delays is proposed with an impulsive vaccination applied at time instants regularly distributed. In this paper we present an analytic solution for the disease free periodic state derived from this model and demonstrate the uniqueness of the obtained solution. A more general model which shares this periodic solution is proposed
    Applied Mathematical Sciences 01/2014; 8(15):701-715.