Rujira Kongnuy
Stability, seasonal structured, SEIR mathematical model, endemic disease state
In this paper, we present a seasonal-structured SEIR model mathematical model. By using theory of the mathematical modeling for infectious disease and methods of ordinary differential equations. The SEIR model is partitioned into compartments of susceptible individuals (S), exposed individuals (E), infectious individuals (I) and recovered individuals (R). It is shown that the disease free equilibrium state is locally asymptotically stable if the basic reproductive number is less than one. It is then proved that the endemic equilibrium state exists when this number is more than one. The numerical results are shown to confirm this study. The control of this disease is discussed in the term of the basic reproductive number.
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