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Temporally Interruptive Interaction Allows Mutual Invasion of Two Competing Species Dispersing in Space

Hiromi Seno (2010)

Mathematical Modelling of Natural Phenomena

With a reaction-diffusion system, we consider the dispersing two-species Lotka-Volterra model with a temporally periodic interruption of the interspecific competitive relationship. We assume that the competition coefficient becomes a given positive constant and zero by turns periodically in time. We investigate the condition for the coexistence of two competing species in space, especially in the bistable case for the population dynamics without dispersion. We could find that the spatial coexistence,...

The Basic Reproduction Number of an Infectious Disease in a Stable Population: The Impact of Population Growth Rate on the Eradication Threshold

H. Inaba, H. Nishiura (2008)

Mathematical Modelling of Natural Phenomena

Although age-related heterogeneity of infection has been addressed in various epidemic models assuming a demographically stationary population, only a few studies have explicitly dealt with age-specific patterns of transmission in growing or decreasing population. To discuss the threshold principle realistically, the present study investigates an age-duration-structured SIR epidemic model assuming a stable host population, as the first scheme to account for the non-stationality of the host population....

The effect of time delay and Hopf bifurcation in a tumor-immune system competition model with negative immune response

Radouane Yafia (2009)

Applicationes Mathematicae

We consider a system of delay differential equations modelling the tumor-immune system competition with negative immune response and three positive stationary points. The dynamics of the first two positive solutions are studied in terms of the local stability. We are particularly interested in the study of the Hopf bifurcation problem to predict the occurrence and stability of a limit cycle bifurcating from the second positive stationary point, when the delay (taken as a parameter) crosses some...

The Effects of HIV-1 Infection on Latent Tuberculosis

Amy L. Bauer, Ian B. Hogue, Simeone Marino, Denise E. Kirschner (2008)

Mathematical Modelling of Natural Phenomena

Tuberculosis is the leading cause of death due to infectious diseases in the world today, and it is increasing due to co-infection with HIV-1, the causative agent of AIDS. Here, we examine the impact that HIV-1 infection has on persons with latent tuberculosis. Based on previous work, we develop a mathematical model of an adaptive immune response in the lung which considers relevant immune effectors such as macrophages, various sub-populations of T-cells, and key cytokines to predict which mechanisms...

The Second Half-With a Quarter of a Century Delay

O. Diekmann, M. Gyllenberg (2008)

Mathematical Modelling of Natural Phenomena

We show how results by Diekmann et al. (2007) on the qualitative behaviour of solutions of delay equations apply directly to a resource-consumer model with age-structured consumer population.

Time discrete 2-sex population model

C. O. A. Sowunmi (2003)

Banach Center Publications

A time-discrete 2-sex model with gestation period is analysed. It is significant that the conditions for local stability of a nontrivial steady state do not require that the expected number of female offspring per female equal unity. This is in contrast to results obtained by Curtin and MacCamy [4] and the author [10].

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