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Global asymptotic stability for a vector disease model with spatial spread

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Summary

We analyze the global behaviour of a vector disease model which involves spatial spread and hereditary effects. This model can be applied to investigate growth and spread of malaria. No immunization is considered. We prove that, if the recovery rate is less than or equal to a threshold value, the disease dies out, otherwise the infectious people density tends to a homogeneous distribution. Our results follow using contracting convexes techniques and agree with the results given by K. L. Cooke for the model without diffusion.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Trento, I-38050, Povo, Italy

    Pierangelo Marcati & M. Assunta Pozio

Authors
  1. Pierangelo Marcati
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  2. M. Assunta Pozio
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Work supported by C.N.R., Grant No. 79.00696.01.

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Marcati, P., Pozio, M.A. Global asymptotic stability for a vector disease model with spatial spread. J. Math. Biology 9, 179–187 (1980). https://doi.org/10.1007/BF00275920

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  • DOI: https://doi.org/10.1007/BF00275920

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