Competitive exclusion and coexistence in a two-strain pathogen model with diffusion.

We consider a two-strain pathogen model described by a system of reaction-diffusion equations. We define a basic reproduction number R0 and show that when the model parameters are constant (spatially homogeneous), if R0 >1 then one strain will outcompete the other strain and drive it to extinction, but if R0 ≤ 1 then the disease-free equilibrium is globally attractive. When we assume that the diffusion rates are equal while the transmission and recovery rates are heterogeneous, then there are two possible outcomes under the condition R0 < 1: 1) Competitive exclusion where one strain dies out.

A second-order characteristic line scheme for solving a juvenile-adult model of amphibians.

In this paper, we develop a second-order characteristic line scheme for a nonlinear hierarchical juvenile-adult population model of amphibians. The idea of the scheme is not to follow the characteristics from the initial data, but for each time step to find the origins of the grid nodes at the previous time level. Numerical examples are presented to demonstrate the accuracy of the scheme and its capability to handle solutions with singularity.

Fitting a structured juvenile-adult model for green tree frogs to population estimates from capture-mark-recapture field data.

We derive point and interval estimates for an urban population of green tree frogs (Hyla cinerea) from capture-mark-recapture field data obtained during the years 2006-2009. We present an infinite-dimensional least-squares approach which compares a mathematical population model to the statistical population estimates obtained from the field data. The model is composed of nonlinear first-order hyperbolic equations describing the dynamics of the amphibian population where individuals are divided into juveniles (tadpoles) and adults (frogs).

Stochastic juvenile--adult models with application to a green tree frog population.

We derive several stochastic models from a deterministic population model that describes the dynamics of age-structured juveniles coupled with size-structured adults. Numerical simulation results of the stochastic models are compared with the solution of the deterministic model. These models are then used to understand the effect of demographic stochasticity on the dynamics of an urban green tree frog (Hyla cinerea) population.

Stability of a delay equation arising from a juvenile-adult model.

We consider a delay equation that has been formulated from a juvenile-adult population model. We give respective conditions on the vital rates to ensure local stability of the positive equilibrium and global stability of the trivial equilibrium. We also show that under certain conditions the equation undergoes a Hopf bifurcation.

A monotone approximation for a size-structured population model with a generalized environment.

We study a nonlinear size-structured population model with an environment general enough to include hierarchy. We also remove the standard requirement that individuals have nonnegative growth rates, which allows the modeling of populations in which individuals may experience a reduction in size. To show existence and uniqueness of the solution to the model, we establish a comparison principle and construct monotone sequences.

A structured erythropoiesis model with nonlinear cell maturation velocity and hormone decay rate.

We develop a quasilinear structured model that describes the regulation of erythropoiesis, the process in which red blood cells are developed. In our model, the maturation velocity of precursor cells is assumed to be a function of the erythropoietin hormone, and the decay rate of this hormone is assumed to be a function of the number of precursor cells, unlike other models which assume these parameters to be constants. Existence-uniqueness results are established and convergence of a finite difference approximation to the unique solution of the model is obtained.

Parameter estimation in a coupled system of nonlinear size-structured populations.

A least squares technique is developed for identifying unknown parameters in a coupled system of nonlinear size-structured populations. Convergence results for the parameter estimation technique are established. Ample numerical simulations and statistical evidence are provided to demonstrate the feasibility of this approach.

Competitive exclusion and coexistence for a quasilinear size-structured population model.

We present a quasilinear size-structured model which describes the dynamics of a population with n competing ecotypes. We assume that the vital rates of each subpopulation depend on the total population due to competition. We provide conditions on the individual rates which guarantee competitive exclusion in the case of closed reproduction (offspring always belongs to the same ecotype as the parent).