Global asymptotic stability for a vector disease model with spatial spread |
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Authors: | Pierangelo Marcati M. Assunta Pozio |
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Affiliation: | (1) Dipartimento di Matematica, Università di Trento, I-38050 Povo, Italy |
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Abstract: | 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.Work supported by C.N.R., Grant No. 79.00696.01. |
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Keywords: | Vector disease model Asymptotic stability Partial delay differential equation Contracting convexes |
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