Abstract
In mathematical models for the spread of infectious diseases, it is well known that there is a threshold phenomenon: if the basic reproduction number R 0 is greater than one, the disease can invade into the susceptible host community, whereas it cannot if R 0 is less than one. The basic reproduction number is the average number of secondary cases produced by one infectious individual during its total infective period, in a population that is in the disease-free steady state (see [1, 3]).
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