Exact solutions to SIR epidemic models via integrable discretization

Author:

Nobe Atsushi1ORCID

Affiliation:

1. Faculty of Political Science and Economics, Waseda University , 1-6-1 Nishiwaseda, Shinjuku, Tokyo 169-8050, Japan

Abstract

An integrable discretization of the SIR model with vaccination is proposed. Through the discretization, the conserved quantities of the continuous model are inherited to the discrete model, since the discretization is based on the intersection structure of the non-algebraic invariant curve defined by the conserved quantities. Uniqueness of the forward/backward evolution of the discrete model is demonstrated in terms of the single-valuedness of the Lambert W function on the positive real axis. Furthermore, the exact solution to the continuous SIR model with vaccination is constructed via the integrable discretization. When applied to the original SIR model, the discretization procedure leads to two kinds of integrable discretization, and the exact solution to the continuous SIR model is also deduced. It is furthermore shown that the discrete SIR model geometrically linearizes the time evolution by using the non-autonomous parallel translation of the line intersecting the invariant curve.

Funder

Japan Society for the Promotion of Science London

Publisher

AIP Publishing

Reference31 articles.

1. A contribution to the mathematical theory of epidemics;Proc. R. Soc. A,1927

2. Asymptotic behavior and stability in epidemic models,1974

3. Transmission and control of arbovirus diseases;Ludwing,1975

4. An age-structured model of pre- and post-vaccination measles transmission;Math. Med. Biol.,1984

5. Epidemic dynamics: Discrete-time and cellular automaton models;Physica A,2003

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