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A host-vector model for malaria with infective immigrants. (English) Zbl 1176.92045
Summary: This paper considers a host-vector mathematical model for the spread of malaria that incorporates recruitment of the human population through a constant immigration, with a fraction of infective immigrants. The model analysis is carried out to find the steady states and their stability. It is found that in the presence of infective immigrant humans, there is no disease-free equilibrium point. However, the model exhibits a unique endemic equilibrium state if the fraction of the infective immigrants $$\phi$$ is positive. When the fraction of infective immigrants approaches a small value, there is a sharp threshold for which the disease can be reduced in the community. The unique endemic equilibrium for which there is a fraction of infective immigrants is globally asymptotically stable.

##### MSC:
 92D30 Epidemiology 34D23 Global stability of solutions to ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations 92C60 Medical epidemiology
##### Keywords:
endemic equilibrium; global stability; infective immigrants
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##### References:
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