Dinâmica de um sistema presa-predador com predador infectado por uma doença

Abstract

The aim of this work is to study the temporal and spatiotemporal evolution of a threedimensional system that describes a predator-prey dynamics, where the predator population can develop an infectious disease. Thus, the predators are split into two subpopulations: susceptible predators and infected predators. The rate at which susceptible become infected is described by a Holling type II functional response giving saturation when the number of susceptible predators increases. We assume that the disease develops only in the predators population and that all are born susceptible, ie, there is no vertical transmission. In the temporal evolution system, described by ordinary di�erential equations, we analyze the asymptotic behavior of the model, describing the necessary conditions for the occurrence of qualitative changes, relating them to the basic reproduction number of predators and the basic reproduction number of the disease. In numerical simulations these changes are graphically described, from the variation of the parameters that determine the predation efficiency of the infected predator and the mortality rate of susceptible and infected predators. Starting from the same local dynamics, we include spatial variation and consider movement by difusion to the population, obtaining a system described by partial diferential equations in which we can observe in addition to the temporal evolution of the spatial evolution of the system, or as populations are distributed spatially over time, when and how invasions occur in the domain. The temporal evolution of the system exhibits complex dynamics such as stable equilibrium, limit cycles, periodic oscillations and aperiodicity. The same dynamics are found in reaction-difusion system, considering that every point of the space represented by x displays a local dynamic . Spatially, invasions were observed in the form of wave fronts, making populations evenly distributed over time.