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Basic reproduction number of SEIRS model on regular lattice

Department of Mathematical and Systems Engineering, Shizuoka University, Hamamatsu 432-8561, Japan

Special Issues: Differential Equations in Mathematical Biology

In this paper we give a basic reproduction number $\mathscr{R}_0$ of an SEIRS model on regular lattice using next-generation matrix approach. Our result is straightforward but differs from the basic reproduction numbers for various fundamental epidemic models on the regular lattice which have been shown so far. Sometimes it is caused by the difference of derivation methods for $\mathscr{R}_0$ although their threshold of infectious rates for epidemic outbreak remain the same. Then we compare our $\mathscr{R}_0$ to the ones by these previous studies from several epidemic points of view.
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Keywords basic reproduction number; lattice model; SEIRS; next-generation matrix; pair approximation

Citation: Kazunori Sato. Basic reproduction number of SEIRS model on regular lattice. Mathematical Biosciences and Engineering, 2019, 16(6): 6708-6727. doi: 10.3934/mbe.2019335


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