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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    • "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.
    Bulletin of entomological research 04/2014; 104(4):1-8. DOI:10.1017/S0007485314000273 · 1.91 Impact Factor
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    • "On the other hand, impulsive problems have been studied not only because of a theoretical interest, but also because they model several phenomena in engineering, physics and life sciences. For example, Nieto and coauthors [57] [60] contributed to the field of population dynamics. An introduction to the theory of impulsive differential equations and its applications can be found in the books [4] [7] [35] [48]. "
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    ABSTRACT: We study the existence of nonnegative solutions for a system of impulsive differential equations subject to nonlinear, nonlocal boundary conditions. The system presents a coupling in the differential equation and in the boundary conditions. The main tool that we use is the theory of fixed point index for compact maps.
    Nonlinear Analysis: Modelling and Control 03/2014; 19(3). DOI:10.15388/NA.2014.3.7 · 1.10 Impact Factor
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    • "The second stage arises from the previous latent state to a fully developed one, in which all symptoms are present and the disease is infectious. The recovered state refers to the moment when the disease is defeated by the organism and becomes immune for a certain period of time, before it becomes susceptible to the disease again [14] [15] [16]. "
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    ABSTRACT: The periodic regime in a SEIR model with a delay is studied in this paper. The model is studied first under a simple set of constant parameters and then a more complex solution is proposed, depending on a set of periodic parameters related to the variable risk of contracting the disease and the different vaccination strategies applied in order to prevent it. Both the periodic parameters and the subpopulations obtained in the periodic solution proposed are defined as generic Fourier series, so the solution is valid for any possible periodic parameters. The stability of such periodic regimes are studied. A complementary numerical simulation of this model under periodic parameters is also included.
    2013 25th Chinese Control and Decision Conference, CCDC 2013, Guiyang; 05/2013
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