Epidemic processes with vaccination and immunity loss studied with the BLUES function method

Jonas Berx and Joseph O. Indekeu

Physica A: Statistical Mechanics and its Applications, 2022, vol. 590, issue C

Abstract: The Beyond-Linear-Use-of-Equation-Superposition (BLUES) function method is extended to coupled nonlinear ordinary differential equations and applied to the epidemiological SIRS model with vaccination. Accurate analytic approximations are obtained for the time evolution of the susceptible and infected population fractions. The results are compared with those obtained with alternative methods, notably Adomian decomposition, variational iteration and homotopy perturbation. In contrast with these methods, the BLUES iteration converges rapidly, globally, and captures the exact asymptotic behavior for long times. The time of the infection peak is calculated using the BLUES approximants and the results are compared with numerical solutions, which indicate that the method is able to generate useful analytic expressions that coincide with the (numerically) exact ones already for a small number of iterations.

Keywords: SIRS model; Matrix BLUES function method; Analytic iteration; Epidemic processes; Optimal choice of linear subsystem; Coupled ODEs (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:590:y:2022:i:c:s0378437121009341

DOI: 10.1016/j.physa.2021.126724

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