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when the lag function r(t) is nearly constant for large /, and has also asked for conditions on the function r under which all solutions approach zero as t—» oo. The purpose of this announcement is to initiate a study of various stability and oscillation problems for equations with perturbed lag functions, and to suggest that a modification of the familiar… (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)

- 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)

In this paper, an attempt is made to estimate the location and period of the limit cycles of Gause-type predator-prey systems in the case when there is a unique unstable positive equilibrium. An annular region which contains all the limit cycles is determined, and an upper bound for the period of the limit cycles is given. Both the annular region and the… (More)

* This investigation was supported by grants from the National Science Foundation and the U. S. Public Health Service (RG-5652). t Postdoctoral fellow of the National Foundation. I Suskind, S. R., C. Yanofsky, and D. M. Bonner, these PROCEEDINGS, 41, 577 (1955). 2 Lerner, P., and C. Yanofsky, J. Bact., 74, 494 (1957). 3 Yanofsky, C., Biochim. Biophys. Acta,… (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)

- 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, 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)

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)