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- Nakul Chitnis, James M Hyman, J. M. Cushing
- Bulletin of mathematical biology
- 2008

We perform sensitivity analyses on a mathematical model of malaria transmission to determine the relative importance of model parameters to disease transmission and prevalence. We compile two sets ofâ€¦ (More)

We study a class of periodically forced, monotone difference equations motivated by applications from population dynamics. We give conditions under which there exists a globally attracting cycle andâ€¦ (More)

- Nakul Chitnis, J. M. Cushing, J. M. Hyman
- SIAM Journal of Applied Mathematics
- 2006

We present an ordinary differential equation mathematical model for the spread of malaria in human and mosquito populations. Susceptible humans can be infected when they are bitten by an infectiousâ€¦ (More)

A defining hypothesis of theoretical ecology during the past century has been that population fluctuations might largely be explained by relatively low-dimensional, nonlinear ecological interactions,â€¦ (More)

- J. M. Cushing
- 1994

The net reproductive value n is defined for a general discrete linear population model with a nonnegative projection matrix. This number is shown to have the biological interpretation of the expectedâ€¦ (More)

- Robert F. Costantino, J. M. Cushing, B. Dennis, Robert A. Desharnais
- Nature
- 1995

SIMPLE nonlinear models can generate fixed points, periodic cycles and aperiodic oscillations in population abundance without any external environmental variation. Another familiar theoretical resultâ€¦ (More)

- Shandelle M. Henson, Robert F. Costantino, J. M. Cushing, B. Dennis, Robert A. Desharnais
- Bulletin of mathematical biology
- 1999

Mathematical models predict that a population which oscillates in the absence of time-dependent factors can develop multiple attracting final states in the advent of periodic forcing. Aâ€¦ (More)

- Robert F. Costantino, J. M. Cushing, B. Dennis, Robert A. Desharnais, Shandelle M. Henson
- Bulletin of mathematical biology
- 1998

Experiments with the flour beetle Tribolium have revealed that animal numbers were larger in cultures grown in a periodically fluctuating volume of medium than in cultures grown in a constant volumeâ€¦ (More)

Abstruct. Our approach to testing nonlinear population theory is to connect rigorously mathematical models with data by means of statistical methods for nonlinear time series. We begin by deriving aâ€¦ (More)

- S M Henson, Robert F. Costantino, J. M. Cushing, Robert A. Desharnais, B Dennis, A A King
- Science
- 2001

Animals and many plants are counted in discrete units. The collection of possible values (state space) of population numbers is thus a nonnegative integer lattice. Despite this fact, manyâ€¦ (More)