Quantifying the Health–Economy Trade-Offs: Mathematical Model of COVID-19 Pandemic Dynamics
<p>Modeling steps.</p> "> Figure 2
<p>COVID-19 patient dynamics.</p> "> Figure 3
<p>Symptom severity transition diagram.</p> "> Figure 4
<p>Diagram <math display="inline"><semantics> <mrow> <mi>p</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>k</mi> </mrow> </semantics></math> in compartment <math display="inline"><semantics> <mrow> <mi>I</mi> </mrow> </semantics></math>.</p> "> Figure 5
<p>Comparison between model predictions and data in the S compartment.</p> "> Figure 6
<p>Comparison between model predictions and data in compartment I.</p> "> Figure 7
<p>Change in MAPE.</p> "> Figure 8
<p>Numerical simulation results without intervention scenario.</p> "> Figure 9
<p>Numerical simulation results of social distancing scenario.</p> "> Figure 10
<p>Numerical simulation results of lockdown scenario.</p> "> Figure 11
<p>Cost estimation results without intervention scenario.</p> "> Figure 12
<p>Cost estimation results with social distancing scenario.</p> "> Figure 13
<p>Cost estimation results with lockdown scenario.</p> ">
Abstract
:1. Introduction
2. Overview
2.1. Epidemiological Mathematical Model
- Rate of change of susceptible to infected per unit time
- Rate of change of infected to recovered per unit time
- Recovered cure rate per unit time
2.2. Discrete Epidemiological Mathematical Model
2.3. Markov Chain
2.4. Mean Absolute Percentage Error (MAPE)
3. Materials and Methods
3.1. Materials
3.2. Methods
4. Results
4.1. Modelling Result
- A person who is susceptible in period ; can be infected in the next period by COVID-19 into the infected group or remain susceptible
- An infected person can have mild symptoms or severe symptoms For the patient is assumed not to require treatment at a health facility such as a hospital. Whereas for the patient is assumed to require medical treatment at a health facility.
- Due to the limited capacity of health facilities, not all patients with severe symptoms of can receive treatment at health facilities. This results in a treated severe symptom group and an untreated severe symptom group .
- Transitions in symptom severity may occur between and ). Since consists of and , symptom severity transitions are described in Figure 3.
- Does not require treatment in a health facility (. It is assumed that in each time period, only a portion of the members of compartment require treatment so that the rest can self-isolate without needing to be treated in health facilities such as hospitals. For groups that are positive for COVID-19 but do not require intensive care in a hospital, the notation is used.
- Needed treatment at a health facility but did not get it, . It is assumed that there are health facilities in each area, but their capacity is limited, resulting in the possibility of patients who need treatment but cannot be treated because of this problem. For groups that are positive for COVID-19 and require intensive care but do not receive it, the notation is used. Equation (12) describes .
- Hospitalized This is a group that needs medical care and receives it. is shown in Equation (13).
4.2. Parameter Estimation Results
- Parameter is estimated using data on the number of West Java hospital beds in 2019.
- The parameter was estimated using daily COVID-19 mortality data. The parameters are calibrated from the parameters using deaths that occurred during quarantine.
- The parameter was estimated using daily COVID-19 recovery data. For parameters , was calibrated from parameter using cures that occurred during quarantine.
- Parameter is estimated using parameters and using Equations (21)–(23).
- Parameter is estimated using parameter and Equations (25)–(27).
4.3. Sensitivity Analysis
4.4. Numerical Simulation Results
5. Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Walløe, L. 3 Medieval and modern bubonic plague: Some clinical continuities. Med. Hist. 2008, 52, 59–73. [Google Scholar] [CrossRef]
- Tumpey, T.M.; Basler, C.F.; Aguilar, P.V.; Zeng, H.; Solórzano, A.; Swayne, D.E.; Cox, N.J.; Katz, J.M.; Taubenberger, J.K.; Palese, P.; et al. Characterization of the reconstructed 1918 Spanish influenza pandemic virus. Science 2005, 310, 77–80. [Google Scholar] [CrossRef] [PubMed]
- Sabin, C.A.; Lundgren, J.D. The natural history of HIV infection. Curr. Opin. HIV AIDS 2013, 8, 311. [Google Scholar] [CrossRef]
- Lam, W.K.; Zhong, N.S.; Tan, W.C. Overview on SARS in Asia and the world. Respirology 2003, 8, S2–S5. [Google Scholar] [CrossRef] [PubMed]
- Ciotti, M.; Ciccozzi, M.; Terrinoni, A.; Jiang, W.C.; Wang, C.B.; Bernardini, S. The COVID-19 pandemic. Crit. Rev. Clin. Lab. Sci. 2020, 57, 365–388. [Google Scholar] [CrossRef] [PubMed]
- Hale, T.; Angrist, N.; Goldszmidt, R.; Kira, B.; Petherick, A.; Phillips, T.; Webster, S.; Cameron-Blake, E.; Hallas, L.; Majumdar, S.; et al. A global panel database of pandemic policies (Oxford COVID-19 Government Response Tracker). Nat. Hum. Behav. 2021, 5, 529–538. [Google Scholar] [CrossRef] [PubMed]
- Izumi, T.; Sukhwani, V.; Surjan, A.; Shaw, R. Managing and responding to pandemics in higher educational institutions: Initial learning from COVID-19. Int. J. Disaster Resil. Built Environ. 2021, 12, 51–66. [Google Scholar] [CrossRef]
- Bai, H.M.; Zaid, A.; Catrin, S.; Ahmed, K.; Ahmed, A. The socio-economic implications of the coronavirus pandemic (COVID-19): A review. Int. J. Surg. 2020, 8, 8–17. [Google Scholar]
- Rahim, F.; Allen, R.; Barroy, H.; Gores, L.; Kutzin, J. COVID-19 Funds in Response to the Pandemic; International Monetary Fund: Washington, DC, USA, 2020. [Google Scholar]
- Sen-Crowe, B.; McKenney, M.; Elkbuli, A. Public health prevention and emergency preparedness funding in the United States: Are we ready for the next pandemic? Ann. Med. Surg. 2020, 59, 242. [Google Scholar] [CrossRef]
- Rudolph, C.W.; Allan, B.; Clark, M.; Hertel, G.; Hirschi, A.; Kunze, F.; Shockley, K.; Shoss, M.; Sonnentag, S.; Zacher, H. Pandemics: Implications for research and practice in industrial and organizational psychology. Ind. Organ. Psychol. 2021, 14, 1–35. [Google Scholar] [CrossRef]
- Bakker, A.; Cai, J.; Zenger, L. Future themes of mathematics education research: An international survey before and during the pandemic. Educ. Stud. Math. 2021, 107, 1–24. [Google Scholar] [CrossRef] [PubMed]
- Adiga, A.; Dubhashi, D.; Lewis, B.; Marathe, M.; Venkatramanan, S.; Vullikanti, A. Mathematical models for covid-19 pandemic: A comparative analysis. J. Indian Inst. Sci. 2020, 100, 793–807. [Google Scholar] [CrossRef] [PubMed]
- Jewell, N.P.; Lewnard, J.A.; Jewell, B.L. Predictive mathematical models of the COVID-19 pandemic: Underlying principles and value of projections. JAMA 2020, 323, 1893–1894. [Google Scholar] [CrossRef] [PubMed]
- Dudine, P.; Hellwig, K.P.; Jahan, S. A Framework for Estimating Health Spending in Response to COVID-19; International Monetary Fund: Washington, DC, USA, 2020. [Google Scholar]
- Torres-Rueda, S.; Sweeney, S.; Bozzani, F.; Naylor, N.R.; Baker, T.; Pearson, C.; Eggo, R.; Procter, S.R.; Davies, N.; Quaife, M.; et al. Stark choices: Exploring health sector costs of policy responses to COVID-19 in low-income and middle-income countries. BMJ Glob. Health 2021, 6, e005759. [Google Scholar] [CrossRef] [PubMed]
- Cook, M.J.; Dri, G.G.; Logan, P.; Tan, J.B.; Flahault, A. COVID-19 Down Under: Australia’s initial pandemic experience. Int. J. Environ. Res. Public Health 2020, 17, 8939. [Google Scholar] [CrossRef]
- McQuade, S.T.; Weightman, R.; Merrill, N.J.; Yadav, A.; Trélat, E.; Allred, S.R.; Piccoli, B. Control of COVID-19 outbreak using an extended SEIR model. Math. Models Methods Appl. Sci. 2021, 31, 2399–2424. [Google Scholar] [CrossRef]
- Samuel, J.; Sinha, S. Optimal control in pandemics. Phys. Rev. E 2021, 103, L010301. [Google Scholar] [CrossRef] [PubMed]
- De Lara-Tuprio, E.P.; Estuar, M.R.; Sescon, J.T.; Lubangco, C.K.; Castillo, R.C.; Teng, T.R.; Tamayo, L.P.; Macalalag, J.M.; Vedeja, G.M. Economic losses from COVID-19 cases in the Philippines: A dynamic model of health and economic policy trade-offs. Humanit. Soc. Sci. Commun. 2022, 9, 111. [Google Scholar] [CrossRef]
- Huppert, A.; Katriel, G. Mathematical modelling and prediction in infectious disease epidemiology. Clin. Microbiol. Infect. 2013, 19, 999–1005. [Google Scholar] [CrossRef]
- Alamo, T.; Reina, D.G.; Millán, P. Data-driven methods to monitor, model, forecast and control covid-19 pandemic: Leveraging data science, epidemiology and control theory. arXiv 2020, arXiv:2006.01731. [Google Scholar]
- Myall, A.; Price, J.; Peach, R.; Abbas, M.; Mookerjee, S.; Ahmad, I.; Ming, D.; Zhu, N.J.; Ramzan, F.; Weisse, A.; et al. Prediction of hospital-onset COVID-19 using networks of patient contact: An observational study. Int. J. Infect. Dis. 2022, 116, S109–S110. [Google Scholar] [CrossRef]
- Jordan, E.; Shin, D.E.; Leekha, S.; Azarm, S. Optimization in the context of COVID-19 prediction and control: A literature review. IEEE Access 2021, 9, 130072–130093. [Google Scholar] [CrossRef] [PubMed]
- Wearing, H.J.; Rohani, P.; Keeling, M.J. Appropriate models for the management of infectious diseases. PLoS Med. 2005, 2, e174. [Google Scholar] [CrossRef] [PubMed]
- Brauer, F.; Fenga, Z.; Castillo-Chaveza, C. Discrete Epidemic Models. Math. Biosci. Eng. 2010, 7, 1–15. [Google Scholar] [PubMed]
- Allen, L.J.; Burgin, A.M. Comparison of deterministic and stochastic SIS and SIR. Math. Biosci. 2000, 163, 1–33. [Google Scholar] [CrossRef] [PubMed]
- Allen, L.J.S. Some Discrete-Time SI, SIR, and SIS Epidemic Models. Math. Biosci. 1994, 124, 83–105. [Google Scholar] [CrossRef] [PubMed]
- Zhou, Y.; Ma, Z. A discrete epidemic model for SARS transmission and control in China. Math. Comput. Model. 2004, 40, 1491–1506. [Google Scholar] [CrossRef] [PubMed]
- Škulj, D. Discrete time Markov chains with interval probabilities. Int. J. Approx. Reason. 2009, 50, 1314–1329. [Google Scholar] [CrossRef]
- Goodwin, P.; Lawton, R. On the asymmetry of the symmetric MAPE. Int. J. Forecast. 1999, 15, 405–408. [Google Scholar] [CrossRef]
- Jawa Barat, P.P. Dashboard Statistik Kasus COVID-19 Provinsi Jawa Barat. Pemerintah Daerah Provinsi Jawa Barat; 2024. Available online: https://dashboard.jabarprov.go.id/id/dashboard-pikobar/trace/statistik (accessed on 21 June 2024).
- Jawa Barat, P.P. Keterisian Tempat Tidur (BOR). Pemerintah Daerah Provinsi Jawa Barat; 2024. Available online: https://dashboard.jabarprov.go.id/id/dashboard-pikobar/treatment/fasyankes (accessed on 21 June 2024).
Parameter | Definition | Value | Details |
---|---|---|---|
Expandable bed fraction | 0.05 | Assumed | |
Bed fraction available at the start of the pandemic | 0.1481 | Estimated | |
Probability of death of patients with severe symptoms who are treated in health facilities | 0.0011 | Estimated | |
Probability of death of patients with severe symptoms who are not treated at a health facility | 0.0017 | Estimated | |
Probability of death of a patient who does not require treatment at a health facility | 0.0006 | Estimated | |
Probability of recovery for patients with severe symptoms who are treated in health facilities | 0.0654 | Estimated | |
Probability of recovery for patients with severe symptoms who are not treated at health facilities | 0.0327 | Estimated | |
Probability of recovery for patients who do not need treatment at a health facility | 0.0981 | Estimated | |
Probability of the patient leaving the compartment | 0.0665 | Estimated | |
Probability of transition from mild to severe symptoms | 0.0095 | Estimated | |
Probability of transition from severe to mild symptoms | 0.0221 | Estimated |
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Pangestu, D.S.; Sukono; Anggriani, N.; Yaacob, N.M. Quantifying the Health–Economy Trade-Offs: Mathematical Model of COVID-19 Pandemic Dynamics. Computation 2024, 12, 139. https://doi.org/10.3390/computation12070139
Pangestu DS, Sukono, Anggriani N, Yaacob NM. Quantifying the Health–Economy Trade-Offs: Mathematical Model of COVID-19 Pandemic Dynamics. Computation. 2024; 12(7):139. https://doi.org/10.3390/computation12070139
Chicago/Turabian StylePangestu, Dhika Surya, Sukono, Nursanti Anggriani, and Najib Majdi Yaacob. 2024. "Quantifying the Health–Economy Trade-Offs: Mathematical Model of COVID-19 Pandemic Dynamics" Computation 12, no. 7: 139. https://doi.org/10.3390/computation12070139