Basic reproduction number of SEIRS model on regular lattice

Kazunori Sato; Kazunori Sato

doi:10.3934/mbe.2019335

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 6708-6727. doi: 10.3934/mbe.2019335

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Basic reproduction number of SEIRS model on regular lattice

Kazunori Sato ^,

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

Received: 01 March 2019 Accepted: 16 July 2019 Published: 25 July 2019

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.
- basic reproduction number,
- lattice model,
- SEIRS,
- next-generation matrix,
- pair approximation
Citation: Kazunori Sato. Basic reproduction number of SEIRS model on regular lattice[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 6708-6727. doi: 10.3934/mbe.2019335

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Abstract

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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