A Mathematical Model for a Disease Outbreak Considering Waning-Immunity Class with Nonlinear Incidence and Recovery Rates

Nursanti Anggriani; Lazarus Kalvein Beay; Fatuh Inayaturohmat; Sanubari Tansah Tresna

doi:10.20944/preprints202308.2065.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 30 August 2023 / Approved: 30 August 2023 / Online: 30 August 2023 (10:29:02 CEST)

In this paper, we constructed and analyzed a modified SIR-type model for the epidemic problem which considering waning-immunity class in the population, with the nonlinear incidence and recovery rates. Depending on the basic reproduction ratio, we investigated conditions for both non-endemic and co-existing cases. The RouthHurwitz criteria is used to verify the local stability of equilibria, whereas for the global stability, the suitable Lyapunov function is selected to analyze the behavioral stability for each equilibria. Moreover, we studied the optimal control problem for this case. Numerically, we give some simulations to support our analitycal findings.

Epidemic model; Basic Reproduction Ratio; Waning immunity; Nonlinear incidence rate; Nonlinear Recovery rate; Lyapunov functions; Optimal control.

Public Health and Healthcare, Health Policy and Services

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A Mathematical Model for a Disease Outbreak Considering Waning-Immunity Class with Nonlinear Incidence and Recovery Rates

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