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Persistence or extinction: Through a mathematical lens
Date:11/12/2012

s precarious even when Ro is less than 1," says Yakubu. "That is, independent of Ro, if the population size decreases below a certain level (the Allee index), then the individuals die faster than they reproduce."

A previous study by the authors showed that even a healthy stable population that is subject to Allee effects would succumb to a small number of infected individuals within a single location or "patch," causing the entire population to become extinct, since small perturbations can reduce population size or density to a level below or close to the Allee threshold.

Transmission of infectious diseases through a population is affected by local population dynamics as well as migration. Thus, when trying to understand the resilience of the ecosystem, the global survival of the species needs to be taken into account, that is, how does movement of animals between different locations affect survival when a disease affects one or more locations? Various infectious disease outbreaks, such as the West Nile virus, Phocine and distemper viruses have been seen to spread rapidly due to migrations.

In this study, the authors extend their previous research by using a multi-patch model to analyze Allee effects within the context of migration between patches. "We investigate the combined effect of a fatal disease, Allee effect and migration on different groups of the same species," Yakubu says. In their conclusions, the host population is seen to become extinct whenever the initial host population density on each patch is lower than the smallest Allee threshold. When the initial host population has a high Allee threshold, the population persists on each patch if the disease transmission rates are small and the growth rate is large. Even in the case of high Allee thresholds, the host population goes extinct if the disease transmission rate is high, and growth rate and disease threshold are small. The presence of a strong Allee effect adds the possibi
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Contact: Karthika Muthukumaraswamy
karthika@siam.org
267-350-6383
Society for Industrial and Applied Mathematics
Source:Eurekalert

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