Version 1
: Received: 30 August 2023 / Approved: 30 August 2023 / Online: 30 August 2023 (10:29:02 CEST)
How to cite:
Anggriani, N.; Beay, L. K.; Inayaturohmat, F.; Tresna, S. T. A Mathematical Model for a Disease Outbreak Considering Waning-Immunity Class with Nonlinear Incidence and Recovery Rates. Preprints2023, 2023082065. https://doi.org/10.20944/preprints202308.2065.v1
Anggriani, N.; Beay, L. K.; Inayaturohmat, F.; Tresna, S. T. A Mathematical Model for a Disease Outbreak Considering Waning-Immunity Class with Nonlinear Incidence and Recovery Rates. Preprints 2023, 2023082065. https://doi.org/10.20944/preprints202308.2065.v1
Anggriani, N.; Beay, L. K.; Inayaturohmat, F.; Tresna, S. T. A Mathematical Model for a Disease Outbreak Considering Waning-Immunity Class with Nonlinear Incidence and Recovery Rates. Preprints2023, 2023082065. https://doi.org/10.20944/preprints202308.2065.v1
APA Style
Anggriani, N., Beay, L. K., Inayaturohmat, F., & Tresna, S. T. (2023). A Mathematical Model for a Disease Outbreak Considering Waning-Immunity Class with Nonlinear Incidence and Recovery Rates. Preprints. https://doi.org/10.20944/preprints202308.2065.v1
Chicago/Turabian Style
Anggriani, N., Fatuh Inayaturohmat and Sanubari Tansah Tresna. 2023 "A Mathematical Model for a Disease Outbreak Considering Waning-Immunity Class with Nonlinear Incidence and Recovery Rates" Preprints. https://doi.org/10.20944/preprints202308.2065.v1
Abstract
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.
Public Health and Healthcare, Health Policy and Services
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.