Abstract
We propose a coupled metapopulation reaction-diffusion model to explain the propagation of the COVID-19 over an island country such as the Philippines. In the main islands, only susceptible, exposed, and asymptomatic individuals are traveling. The model takes into account the mean daily movement and the transfers and is parametrized using data on the confirmed cases and deaths from the Philippines. To proceed, we set up the system of partial and ordinary differential equations whereby the basic reproduction number, \(\mathcal {R}_0\), is obtained. Next, we simulate the spatial spread of COVID-19 during the first 140 days of infection using a combination of level-set and finite difference methods. Afterward, scenarios of lockdown and unlockdown were studied. Our results displayed a remarkably close similarity to what happened in the Philippines during its first 140 days.
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COVID-19: an ongoing public health crisis in the Philippines. Lancet Reg Health—Western Pac 9:100160 (2021)
Philippines COVID: 1,315,639 Cases and 22,788 Deaths—Worldometer (2021)
Arcede JP, Caga-anan RL, Mentuda CQ, Mammeri Y (2020) Accounting for symptomatic and asymptomatic in a seir-type model of covid-19. Math Mod Nat Pheno
Brauer F, Castillo-Chavez C (2012) Mathematical models in population biology and epidemiology. Springer, New York, NY
Crisostomo S, Romero A, Mendez C (2020) Nine mindanao provinces emerging as COVID-19 Hotspots; Gov’t seeks ways to open up the economy
Dancel R (2020) Covid-19 ‘hot spot’ Cebu City to remain on lockdown; manila restrictions eased further, July 2020
Danon L, Brooks-Pollock E, Bailey M, Keeling MJ (2020) A spatial model of covid-19 transmission in england and wales: early spread and peak timing. MedRxiv
Fitzgibbon WE, Langlais M, Morgan JJ (2007) A mathematical model for indirectly transmitted diseases. Math Biosci 206:233–248
Gardner L (2020) Modeling the spreading risk of 2019-ncov. Technical report, Center for Systems Science and Engineering, Johns Hopkins University
Giuliani D, Dickson MM, Espa G, Santi F (2020) Modelling and predicting the spatio-temporal spread of coronavirus disease 2019 (covid-19) in Italy
Gonzales C (2021) DOH reports 8 more cases of UK Covid-19 variant; total in PH now 25, Feb 2021
Kahambing JGS (2021) Psychosocial wellbeing and Stress Coping Strategies during COVID-19 of Social Workers in Southern Leyte, Philippines. Asian J Psychiatr 102733 (2021)
Lauer SA, Grantz KH, Bi Q, Jones FK, Zheng Q, Meredith HR, Azman AS, Reich NG, Lessler J (2019) The incubation period of coronavirus disease, (covid-19) from publicly reported confirmed cases: estimation and application. Ann Int Med 03:2020
Liu Z, Magal P, Seydi O, Webb G (2020) Predicting the cumulative number of cases for the covid-19 epidemic in china from early data. Math Bios Eng 17:3040
Mammeri Y (2020) A reaction-diffusion system to better comprehend the unlockdown: application of seir-type model with diffusion to the spatial spread of covid-19 in France. Comput Math Biophys 8(1):102–113
McCormack RK, Allen LJS (2007) Multi-patch deterministic and stochastic models for wildlife diseases. J Bio Dyn 63–85
Mercado NA (2020) Makati, Quezon City remain as virus hotspots; localized lockdowns pushed, Dec 2020
Osher S, Fedkiw R (2002) Level set methods and dynamic implicit surfaces. Springer, New York
Panovska-Griffiths J (2020) Can mathematical modelling solve the current Covid-19 crisis? BMC Publ Health 20(1):551
Shigesada N, Kawasaki K (1997) Biological invasions: theory and practice. Oxford University Press
van den Driessche P, Watmough J (2000) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180(1–2):29–48
Wu JT, Leung K, Leung GM (2020) Nowcasting and forecasting the potential domestic and international spread of the 2019-NCOV outbreak originating in Wuhan, China: a modelling study. The Lancet 395(10225):689–697
Acknowledgements
This work was supported by DOST-PCHRD under the project Understanding COVID-19 Pandemic Situation in Caraga Region through Epidemiological Models and Resiliency Studies (UnCOVER) 2020. YM is funded by the Agence National de la Recherche and Région Hauts-de-France, projet Space-covid ANR Résilience.
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Arcede, J.P., Basañez, R.C., Mammeri, Y. (2022). Hybrid Modeling of COVID-19 Spatial Propagation over an Island Country. In: Srinivas, R., Kumar, R., Dutta, M. (eds) Advances in Computational Modeling and Simulation. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-16-7857-8_7
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