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Pathogen Competition and Coexistence and the Evolution of Virulence

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Mathematics for Life Science and Medicine

Part of the book series: Biological and Medical Physics, Biomedical Engineering ((BIOMEDICAL))

Summary

Competition between different strains of a micro-parasite which provide complete cross-protection and cross-immunity against each other selects for maximal basic replacement ratio if, in the absence of the disease, the host population is exclusively limited in its growth by a nonlinear population birth rate. For mass action incidence, the principle of R0 maximization can be extended to exponentially growing populations, if the exponential growth rate is small enough that the disease can limit population growth. For standard incidence, though not in full extent, it can be extended to populations which, without the disease, either grow exponentially or are growth-limited by a nonlinear population death rate, provided that disease prevalence is low and there is no immunity to the disease. If disease prevalence is high, strain competition rather selects for low disease fatality. A strain which would go extinct on its own can coexist with a more virulent strain by protecting from it, if it has strong vertical transmission.

partially supported by NSF grant 0314529

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  1. Department of Mathematics and Statistics, Arizona State University, USA

    Horst R. Thieme

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  1. Faculty of Engineering, Department of Systems Engineering, Shizuoka University, Hamamatsu 3-5-1, 432-8561, Shizuoka, Japan

    Yasuhiro Takeuchi  & Kazunori Sato  & 

  2. Department of Biology, Kyushu University, 812-8581, Fukuoka, Japan

    Yoh Iwasa

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Thieme, H.R. (2007). Pathogen Competition and Coexistence and the Evolution of Virulence. In: Takeuchi, Y., Iwasa, Y., Sato, K. (eds) Mathematics for Life Science and Medicine. Biological and Medical Physics, Biomedical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34426-1_6

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