Competition between low and high pathogenicity avian influenza in a two-patch system.

Over the last decade, the epidemiology of avian influenza has undergone a significant transformation. Not only have we seen an increase in the number of outbreaks of the deadly strain known as highly pathogenic avian influenza (HPAI), but the number of birds infected, and the cost of control has risen drastically. Live poultry markets play a huge role in the bird to bird transmission of avian influenza. We develop a two patch model to determine the competition between low pathogenic avian influenza (LPAI) and HPAI strains when migration is present. We define the two patches as live poultry markets in which the patches are connected through migration. We use a system of differential equations to analyze the existence-stability of the LPAI and HPAI equilibria and established results for the critical threshold R0. We observed that in general migration in both directions increases the abundance of poultry infected with the HPAI strain. Migration promotes the coexistence in Patch 2 while in Patch 1 the region of coexistence fluctuates when migration is active between both patches.

An age-structured epidemic model of rotavirus with vaccination.

The recent approval of a rotavirus vaccine in Mexico motivates this study on the potential impact of the use of such a vaccine on rotavirus prevention and control. An age-structured model that describes the rotavirus transmission dynamics of infections is introduced. Conditions that guarantee the local and global stability analysis of the disease-free steady state distribution as well as the existence of an endemic steady state distribution are established. The impact of maternal antibodies on the implementation of vaccine is evaluated. Model results are used to identify optimal age-dependent vaccination strategies. A convergent numerical scheme for the model is introduced but not implemented. This paper is dedicated to Prof. K. P. Hadeler, who continues to push the frontier of knowledge in mathematical biology.

Exponential growth in age-structured two-sex populations.

We consider a continuous age-structured two-sex population model which is given by a semilinear system of partial differential equations with nonlocal boundary conditions and is a simpler case of Fredrickson-Hoppensteadt model. The non-linearity is introduced by a source term, called from its physical meaning, the marriage function. The explicit form of the marriage function is not known; however, there is an understanding among the demographers about the properties it should satisfy. We have shown that the homogeneity property of the non-linearity leads to the fact that the system supports exponentially growing persistent solutions using a general form of the marriage function and its properties. This suggests that the model can be viewed as a possible extension of the one-sex stable population theory to monogamously mating two-sex populations.

A two-sex age-structured population model: well posedness.

PIP: "In this paper we consider a two-sex population model proposed by Hoppenstead. We do not assume any special form of the mating function. We address the problem of existence and uniqueness of continuous and classical solutions. We give sufficient conditions for continuous solutions to exist globally and we show that they have in fact a directional derivative in the direction of the characteristic lines and satisfy the equations of the model with the directional derivative replacing the partial derivatives. The existence of classical solutions is established with mild assumptions on the vital rates." (EXCERPT)^ieng