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- K Cooke, P van den Driessche, X Zou
- Journal of mathematical biology
- 1999

A population with birth rate function B(N) N and linear death rate for the adult stage is assumed to have a maturation delay T>0. Thus the growth equation N'(t)=B(N(t-T)) N(t-T) e(-)d(1)T- dN(t) governs the adult population, with the death rate in previous life stages d(1)>==0. Standard assumptions are made on B(N) so that a unique equilibrium N(e) exists.… (More)

- K L Cooke, P van den Driessche
- Journal of mathematical biology
- 1996

A disease transmission model of SEIRS type with exponential demographic structure is formulated. All newborns are assumed susceptible, there is a natural death rate constant, and an excess death rate constant for infective individuals. Latent and immune periods are assumed to be constants, and the force of infection is assumed to be of the standard form,… (More)

- S Busenberg, K L Cooke
- Journal of mathematical biology
- 1980

Models of epidemics that lead to delay differential equations often have subsidiary integral conditions that are imposed by the interpretation of these models. The neglect of these conditions may lead to solutions that behave in a radically different manner from solutions restricted to obey them. Examples are given of such behavior, including cases where… (More)

- S Busenberg, K L Cooke
- Theoretical population biology
- 1988

The transmission of Keystone virus in the mosquito Aedes atlanticus and of Rickettsia rickettsii in the tick Dermacentor andersoni is modeled and analyzed. Both of these infections can be transmitted vertically from an infective parent to newborn offspring as well as horizontally via direct or indirect contacts with infected individuals. The vertical… (More)

In this paper we will study in a qualitative way discrete single species population models including harvesting. The class of models under consideration is quite general. In fact, we will study models with fixed parameter values. However, the obtained results do have implications for the models if one varies the parameters slightly. The models with… (More)

- Simon A. Levin, Fred Brauer, +20 authors Angel F. Capurro
- 2007

Intraspecific competition, dispersal and disease dynamics in discrete-time patchy environments The impact of long-range dispersal on the rate of spread in population and epidemic models

A general model is considered for treatment and behaviour change of the Human Immunodeficiency Virus (HIV) infected in a highly sexually active core group of female commercial sex workers (CSWs) and a 'bridge population' of young unpartnered males. In this model, the spread of HIV/AIDS in the community is carried out mainly through the sexual interaction… (More)

- S Busenberg, K L Cooke, M A Pozio
- Journal of mathematical biology
- 1983

A model is presented of a disease that can be transmitted directly from parent to offspring (vertical transmission) as well as through contact with infectives. A global stability analysis is given for the basic model and the epidemiological effects of vertical transmission are discussed. The effects of the addition of maturation and incubation delays as… (More)

- Kenneth L. Cooke
- 2003

An important consideration in the nonlinear predator-prey problem of Lotka-Volterra type is the determination of the period. This paper gives a general expression for the period in terms of the given parameters in the Lotka-Volterra system. We also discuss the qualitative behavior of the period related to the energy level of the Lotka-Volterra system.