Optimal control on COVID-19 eradication program in Indonesia under the effect of community awareness

Dipo Aldila; Meksianis Z. Ndii; Brenda M. Samiadji; Dipo Aldila; Meksianis Z. Ndii; Brenda M. Samiadji

doi:10.3934/mbe.2020335

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 6355-6389. doi: 10.3934/mbe.2020335

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Optimal control on COVID-19 eradication program in Indonesia under the effect of community awareness

1.
Department of Mathematics, Universitas Indonesia, Depok 16424, Indonesia
2.
Department of Mathematics, University of Nusa Cendana, Kupang-NTT 85361, Indonesia

Received: 15 July 2020 Accepted: 15 September 2020 Published: 23 September 2020

A total of more than 27 million confirmed cases of the novel coronavirus outbreak, also known as COVID-19, have been reported as of September 7, 2020. To reduce its transmission, a number of strategies have been proposed. In this study, mathematical models with nonpharmaceutical and pharmaceutical interventions were formulated and analyzed. The first model was formulated without the inclusion of community awareness. The analysis focused on investigating the mathematical behavior of the model, which can explain how medical masks, medical treatment, and rapid testing can be used to suppress the spread of COVID-19. In the second model, community awareness was taken into account, and all the interventions considered were represented as time-dependent parameters. Using the center-manifold theorem, we showed that both models exhibit forward bifurcation. The infection parameters were obtained by fitting the model to COVID-19 incidence data from three provinces in Indonesia, namely, Jakarta, West Java, and East Java. Furthermore, a global sensitivity analysis was performed to identify the most influential parameters on the number of new infections and the basic reproduction number. We found that the use of medical masks has the greatest effect in determining the number of new infections. The optimal control problem from the second model was characterized using the well-known Pontryagin's maximum principle and solved numerically. The results of a cost-effectiveness analysis showed that community awareness plays a crucial role in determining the success of COVID-19 eradication programs.
- COVID-19,
- community awareness,
- medical mask,
- rapid testing,
- hospitalization,
- quarantine,
- basic reproduction number,
- forward bifurcation,
- optimal control
Citation: Dipo Aldila, Meksianis Z. Ndii, Brenda M. Samiadji. Optimal control on COVID-19 eradication program in Indonesia under the effect of community awareness[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 6355-6389. doi: 10.3934/mbe.2020335

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Abstract

A total of more than 27 million confirmed cases of the novel coronavirus outbreak, also known as COVID-19, have been reported as of September 7, 2020. To reduce its transmission, a number of strategies have been proposed. In this study, mathematical models with nonpharmaceutical and pharmaceutical interventions were formulated and analyzed. The first model was formulated without the inclusion of community awareness. The analysis focused on investigating the mathematical behavior of the model, which can explain how medical masks, medical treatment, and rapid testing can be used to suppress the spread of COVID-19. In the second model, community awareness was taken into account, and all the interventions considered were represented as time-dependent parameters. Using the center-manifold theorem, we showed that both models exhibit forward bifurcation. The infection parameters were obtained by fitting the model to COVID-19 incidence data from three provinces in Indonesia, namely, Jakarta, West Java, and East Java. Furthermore, a global sensitivity analysis was performed to identify the most influential parameters on the number of new infections and the basic reproduction number. We found that the use of medical masks has the greatest effect in determining the number of new infections. The optimal control problem from the second model was characterized using the well-known Pontryagin's maximum principle and solved numerically. The results of a cost-effectiveness analysis showed that community awareness plays a crucial role in determining the success of COVID-19 eradication programs.

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