We derive from a structured population model a system of delay differential equations describing the interaction of five subpopulations, namely susceptible and infected adult and juvenile reservoirs and infected adult vectors, for a vector borne disease with particular reference to West Nile virus, and we also incorporate spatial movements by considering the analogue reactiondiffusion systems w...

We consider a spiked population model, proposed by Johnstone, whose population eigenvalues are all unit except for a few fixed eigenvalues. The question is to determine how the sample eigenvalues depend on the non-unit population ones when both sample size and population size become large. This paper completely determines the almost sure limits for a general class of samples.

We propose a method for partially discretizing a model of an agedependent population dynamics with an additional structure whose growth rate is age-dependent. We give theoretical conditions under which a second order accuracy arises. A priori estimates are obtained. The main result indicates that the sum of these errors converges and is of second order accuracy.

The early life history 7 Abstract The relationship between the biomass of reproductively mature individuals (spawning stock) and the resulting offspring added to the population (recruitment), the stock–recruitment relationship, is a fundamental and challenging problem in all of population biology. The steepness of this relationship is commonly defined as the fraction of recruitment from an unfi...

We study the qualitative properties of degenerate diiusion equations used to describe dispersal processes in population dynamics. For systems of interacting populations, the forms of the diiusion models used determine if the population will intermix or remain disjoint (segregated). The dynamics and stability of segregation boundaries between competing populations is analyzed. General population...

We consider a nonlinear structured population model with a distributed recruitment term. The question of the existence of non-trivial steady states can be treated (at least!) in three different ways. One approach is to study spectral properties of a parametrized family of unbounded operators. The alternative approach, on which we focus here, is based on the reformulation of the problem as an in...

Model Evolution of Voltage over Time Consider a group of interacting populations of neurons. Equation 1 describes the evolution over time of the membrane voltages for the ith ensemble. Table 1 explains the remaining variables.

We study the responses of discretely reproducing populations to periodic fluctuations in three parameters, the carrying capacity and two demographic characteristics of the species (three parameters). We prove that small 2-periodic fluctuations of the three parameters generate 2-cyclic oscillations of the population. We develop a signature function for predicting the responses of populations to ...