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Modeling disease spread via transport-related infection by a delay differential equation. (English) Zbl 1194.34111
Summary: A delayed SIS model is developed to describe the effect of transport-related infection, where time delay arises very naturally and the basic reproduction number $$R_0$$ can be calculated. It is shown that this number characterizes the disease transmission dynamics: if $$R_0<1$$, there exists only a disease-free equilibrium which is globally asymptotically stable; and if $$R_0>1$$, then there is a disease-endemic equilibrium and the disease persists. Analysis of the dependence of $$R_0$$ on the transport-related infection parameters shows that an outbreak can arise purely due to this transport-related infection.

##### MSC:
 34D23 Global stability of solutions to ordinary differential equations 92D30 Epidemiology 34K20 Stability theory of functional-differential equations
##### Keywords:
transport-related infection; stability; delay; permanence
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##### References:
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