Abstract
A non-autonomous epidemic dynamical system, in which we include variable susceptibility, is proposed. Some threshold conditions are derived which determine whether or not the disease will go to extinction. Some new threshold values, [Formula: see text], [Formula: see text] and [Formula: see text], are deduced for this general time-dependent system such that when [Formula: see text] is greater than 0, the disease is endemic in the sense of permanence and when one of the threshold values [Formula: see text] and [Formula: see text] is less than 0, the disease will die out. As an application of these results, the basic reproductive number ℛ0will be given if all the coefficients are periodic with common period. In addition, ℛ0< 1 implies the global stability of the disease-free periodic solution. Some corollaries are given for periodic and almost-periodic cases. The theoretical results are confirmed by a special example and numerical simulations.
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