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

Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain
Nonlinear Analysis Real World Applications (Impact Factor: 2.52). 09/2008; 9(4):1714-1726. DOI: 10.1016/j.nonrwa.2007.05.004


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.

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    • "The main purpose of this paper is to formulate and investigate an epidemiological model for the bio-control of a pest. In fact, the theoretical investigation and its application analysis can be found in almost every field [32] [33] [34] [35] [36] [37] [38] [39] [40]. This pest population is assumed to grow according to a logistic curve in the absence of disease [41] [42]. "
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    ABSTRACT: In this paper, we investigate the pest control model with population dispersal in two patches and impulsive effect. By exploiting the Floquet theory of impulsive differential equation and small amplitude perturbation skills, we can obtain that the susceptible pest eradication periodic solution is globally asymptotically stable if the impulsive periodic τ is less than the critical value τ0 . Further, we also prove that the system is permanent when the impulsive periodic τ is larger than the critical value τ0. Hence, in order to drive the susceptible pest to extinction, we can take impulsive control strategy such that τ < τ0 according to the effect of the viruses on the environment and the cost of the releasing pest infected in a laboratory. Finally, numerical simulations validate the obtained theoretical results for the pest control model with population dispersal in two patches and impulsive effect.
    Full-text · Article · Sep 2014 · Journal of Computational Science
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    • "Today, a great arsenal is available to control insect pests but to be effective, substances should target the most susceptible stage to maximize effectiveness and thus minimize the number of applications (Thacker, 2002; Van Driesche et al., 2008). Accurate prediction of the insect growth rate and timings of emergence is therefore essential for developing effective pest management strategies and mathematical models greatly help in determining insect emergence dates and population size in order to construct optimal treatment schedules (Li et al., 2004; Yonow et al., 2004; Moravie et al., 2006; Georgescu & Morosanu, 2007; Zhang et al., 2008; Jiao et al., 2009; Ainseba et al., 2011; Baumann et al., 2013). Models sometimes fail to provide useful predictions for pest management due to the lack of basic knowledge of pest ecology (Shaffer & Gold, 1985; Ainseba et al., 2011). "
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    ABSTRACT: Effective pest management with lower amounts of pesticides relies on accurate prediction of insect pest growth rates. Knowledge of the factors governing this trait and the resulting fitness of individuals is thus necessary to refine predictions and make suitable decisions in crop protection. The European grapevine moth, Lobesia botrana, the major pest of grapes in Europe, is responsible for huge economic losses. Larvae very rarely leave the grape bunch on which they were oviposited and thus cannot avoid intraspecific competition. In this study, we determined the impact of intraspecific competition during the larval stage on development and adult fitness in this species. This was tested by rearing different numbers of larvae on an artificial diet and measuring developmental and reproductive life history traits. We found that intraspecific competition during larval development has a slight impact on the fitness of L. botrana. The principal finding of this work is that larval density has little effect on the life history traits of survivors. Thus, the timing of eclosion, duration of subsequent oviposition, fecundity appears to be more uniform in L. botrana than in other species. The main effect of larval crowding was a strong increase of larval mortality at high densities whereas the probability of emergence, sex ratio, pupal mass, fecundity and longevity of mated females were not affected by larval crowding. Owing to increased larval mortality at high larval densities, we hypothesized that mortality of larvae at high densities provided better access to food for the survivors with the result that more food was available per capita and there were no effect on fitness of survivors. From our results, larval crowding alters the reproductive capacity of this pest less than expected but this single factor should now be tested in interaction with limited resources in the wild.
    Full-text · Article · Apr 2014 · Bulletin of entomological research
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    • "Spraying pesticides and releasing natural enemies are instantaneous; these phenomena can be described as the impulsive differential equations. In recent decades, the theoretical research on the impulsive differential equation has represented a significant development and has been widely used in various mathematical ecological models [3] [4] [5] [6] [7] [8] [9] [10] [11] and many scholars made a deep analysis of the impulsive differential ecological system at a fixed time and have got some important products [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]. However, in the actual process of pest control, relevant measures will be used according to pest quantity and its damage to crops, which is the state impulsive differential system. "
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    ABSTRACT: According to integrated pest management strategies, we construct and investigate the dynamics of a Holling-Tanner predator-prey system with state dependent impulsive effects by releasing natural enemies and spraying pesticide at different thresholds. Applying the Dulacs criterion, the global stability of the positive equilibrium in the system without impulsive effect is discussed. By using impulsive differential equation geometry theory and the method of successor functions, we prove the existence of periodic solution of the system with state dependent impulsive effects. Furthermore, the stability conditions of periodic solutions are obtained. Some simulations are exerted to illustrate the feasibility of our main results.
    Full-text · Article · Mar 2014 · Abstract and Applied Analysis
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