### Mathematical Biosciences and Engineering

2019, Issue 6: 6708-6727. doi: 10.3934/mbe.2019335
Research article Special Issues

# Basic reproduction number of SEIRS model on regular lattice

• 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.

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

### Related Papers:

• 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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