A delayed epidemic model with stage-structure and pulses for pest management strategy
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.
- SourceAvailable from: Manuel De la Sen[show abstract] [hide abstract]
ABSTRACT: The equilibrium states of a mathematical model of an infectious disease are studied in this paper under variable parameters. A simple SEIR model with a delay is presented under a set of parameters vary-ing periodically, characteristic to the seasonality of the disease. The final equilibrium state, determined by these parameters, is obtained with a general method based on a Fourier analysis of the dynamics of the subpopulations proposed in this paper. Then the stability of these equilibrium states for the general and some particular cases will be contemplated, and simulations will be made in order to confirm the predictions.Applied Mathematical Sciences 01/2013; 7:773-789.
- [show abstract] [hide abstract]
ABSTRACT: After a pest develops resistance to a pesticide, switching between different unrelated pesticides is a common management option, but this raises the following questions: (1) What is the optimal frequency of pesticide use? (2) How do the frequencies of pesticide applications affect the evolution of pesticide resistance? (3) How can the time when the pest population reaches the economic injury level (EIL) be estimated and (4) how can the most efficient frequency of pesticide applications be determined? To address these questions, we have developed a novel pest population growth model incorporating the evolution of pesticide resistance and pulse spraying of pesticides. Moreover, three pesticide switching methods, threshold condition-guided, density-guided and EIL-guided, are modelled, to determine the best choice under different conditions with the overall aim of eradicating the pest or maintaining its population density below the EIL. Furthermore, the pest control outcomes based on those three pesticide switching methods are discussed. Our results suggest that either the density-guided or EIL-guided method is the optimal pesticide switching strategy, depending on the frequency (or period) of pesticide applications.Mathematical biosciences 07/2013; · 1.30 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