Exact solution for a discrete-time SIR model

被引：0

作者：

Lemos-Silva, Marcia ^{[1
]}

Vaz, Sandra ^{[2
]}

Torres, Delfim F. M. ^{[1
,3
]}

机构：

[1] Univ Aveiro, Ctr Res & Dev Math & Applicat CIDMA, Dept Math, P-3810193 Aveiro, Portugal

[2] Univ Beira Interior, Ctr Math & Applicat CMA UBI, Dept Math, P-6201001 Covilha, Portugal

[3] Univ Cape Verde Uni CV, Fac Sci & Technol FCT, Res Ctr Exact Sci CICE, P-7943010 Praia, Cape Verde

来源：

APPLIED NUMERICAL MATHEMATICS | 2025年 / 207卷

关键词：

Compartmental models; Nonlinear epidemiological systems; Mickens method; Local stability; Exact solution of a SIR discrete-time system; Consistent discretization; FINITE-DIFFERENCE SCHEMES;

D O I：

10.1016/j.apnum.2024.09.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a nonstandard finite difference scheme for the Susceptible-Infected-Removed (SIR) continuous model. We prove that our discretized system is dynamically consistent with its continuous counterpart and we derive its exact solution. We end with the analysis of the long-term behavior of susceptible, infected and removed individuals, illustrating our results with examples. In contrast with the SIR discrete-time model available in the literature, our new model is simultaneously mathematically and biologically sound.

引用

页码：339 / 347

页数：9

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