Vaccination effect conjoint to fraction of avoided contacts for a Sars-Cov-2 mathematical model

Yıl 2021, Cilt: 1 Sayı: 2, 56 - 66, 30.12.2021

Stefania Allegretti Iulia Martina Bulai Roberto Marino Margherita Anna Menandro Katia Parisi

https://doi.org/10.53391/mmnsa.2021.01.006

Cited By: 22

Öz

In this paper, we consider a modified SIR (susceptible-infected-recovered/removed) model that describes the evolution in time of the infectious disease caused by Sars-Cov-2 (Severe Acute Respiratory Syndrome-Coronavirus-2). We take into consideration that this disease can be both symptomatic and asymptomatic. By formulating a suitable mathematical model via a system of ordinary differential equations (ODEs), we investigate how the vaccination rate and the fraction of avoided contacts affect the population dynamics.

Anahtar Kelimeler

SIR model, asymptomatic cases, avoided contacts, vaccination effect, COVID-19

Kaynakça

• https://www.who.int/health-topics/coronavirus.
• Bernoulli, D., Blower, S. An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it. Reviews in medical virology,14(5), 275-288, (2004).
• Rahimi, I., Chen, F. and Gandomi, A.H. A review on COVID-19 forecasting models. Neural Computing and Applications, 1-11, (2021).
• Akgül, A., Ahmed, N., Raza, A., et al. New applications related to Covid-19.Results in Physics,20, 103663, (2021).
• Farman, M., Akgül, A., Ahmad, A., Baleanu, D., Saleem, M.U. Dynamical Transmission of Coronavirus Model with Analysis and Simulation. CMES-Computer Modeling in Engineering and Sciences, 127(2), 753–769, (2021).
• Amico, E., Bulai, I.M. How political choices shaped Covid connectivity: the Italian case study, Plos One, (2021).
• Zeb, A., Alzahrani, E., Erturk, V.S., Zaman, G. Mathematical model for Coronavirus Disease 2019 (COVID-19) Containing Isolation Class. BioMed Research International, (2020).
• Zhang, Z., Zeb, A., Hussain, S., Alzahrani, E. Dynamics of COVID-19 mathematical model with stochastic perturbation. Advances in Difference Equations, 2020(1), 1-12, (2020).
• Naik, P.A., Yavuz, M., Qureshi, S., Zu, J. & Townley, S. Modeling and analysis of COVID-19 epidemics with treatment in fractional derivatives using real data from Pakistan. The European Physical Journal Plus, 135(10), 1-42, (2020).
• Zhang, Z., Zeb, A., Egbelowo, O.F., Erturk, V.S. Dynamics of a fractional order mathematical model for COVID-19 epidemic. Advances in Difference Equations, 2020(1), 1-16, (2020).
• Özköse, F., Yavuz, M. Investigation of interactions between COVID-19 and diabetes with hereditary traits using real data: A case study in Turkey. Computers in Biology and Medicine, 105044, (2021).
• Nazir, G., Zeb, A., Shah, K., Saeed, T., Khan, R.A. & Khan, S.I.U. Study of COVID-19 mathematical model of fractional order via modified Euler method. Alexandria Engineering Journal, 60(6), 5287-5296, (2021).
• Bushnaq, S., Saeed, T., Torres, D.F.M., Zeb, A. Control of COVID-19 dynamics through a fractional-order model. Alexandria Engineering Journal, 60(4), 3587-3592, (2021).
• Yavuz, M., Coşar, F.Ö, Günay, F., Özdemir, F.N. A new mathematical modeling of the COVID-19 pandemic including the vaccination campaign. Open Journal of Modelling and Simulation, 9(3), 299-321, (2021).
• Zhang, Z., Zeb, A., Alzahrani, E. & Iqbal, S. Crowding effects on the dynamics of COVID-19 mathematical model. Advances in Difference Equations, 2020(1), 1-13, (2020).
• Li, X.P., Al Bayatti, H., Din, A. & Zeb, A. A vigorous study of fractional order COVID-19 model via ABC derivatives. Results in Physics, 29, 104737, (2021).
• Guan, J., Wei, Y., Zhao, Y., Chen, F. Modeling the transmission dynamics of COVID-19 epidemic: a systematic review. Journal of Biomedical Research, 34(6), 422-430, (2020).
• Atangana, A., Araz, S.İ. Mathematical model of COVID-19 spread in Turkey and South Africa: theory, methods, and applications. Advances in Difference Equations, 2020(1), 1-89, (2020).
• Amaro, J.E., Dudouet, J., Orce, J.N. Global analysis of the COVID-19 pandemic using simple epidemiological models. Applied Mathematical Modelling, 90, 995-1008, (2021).
• Buonomo, B., Della Marca, R. Effects of information-induced behavioural changes during the COVID-19 lockdowns: the case of Italy. Royal Society Open Science, 7(10), 201635, (2020).
• Zhu, H., Li, Y., Jin, X., Huang, J., Liu, X., Qian, Y., Tan, J. Transmission dynamics and control methodology of COVID-19: A modeling study. Applied Mathematical Modelling, 89(2), 1983-1998, (2021).
• Pellis, L., et al. & University of Manchester COVID-19 Modelling Group. Challenges in control of Covid-19: short doubling time and long delay to effect of interventions. Philosophical Transactions of the Royal Society B, 376(1829), 20200264, (2021).
• Sun, D., Duan, L., Xiong, J. & Wang, D. Modeling and forecasting the spread tendency of the COVID-19 in China. Advances in Difference Equations, 2020(1), 1-16, (2020).
• Giordano, G., Blanchini, F., Bruno, R., Colaneri, P., Di Filippo, A., Di Matteo, A. & Colaneri, M. Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy. Nature medicine, 26(6), 855–860, (2020).
• Pedersen, M.G., Meneghini, M. Data-driven estimation of change points reveals correlation between face mask use and accelerated curtailing of the first wave of the COVID-19 epidemic in Italy. Infectious Diseases, 53(4), 243-251, (2021).
• Viguerie, A., et al. Simulating the spread of COVID-19 via a spatially-resolved susceptible–exposed–infected–recovered–deceased (SEIRD) model with heterogeneous diffusion. Applied Mathematics Letters, 111, 106617, (2021).
• Ferguson, N., et al. Report 9: Impact of non-pharmaceutical interventions (NPIs) to reduce COVID19 mortality and healthcare demand. Imperial College London, (2020).
• Chowdhury, R., Heng, K., Shawon, M.S.R., Goh, G., Okonofua, D., Ochoa-Rosales, C., ... & Franco, O.H. Dynamic interventions to control COVID-19 pandemic: a multivariate prediction modelling study comparing 16 worldwide countries. European journal of epidemiology, 35(5), 389-399, (2020).
• Jiao, J., Liu, Z., Cai, S. Dynamics of an SEIR model with infectivity in incubation period and homestead-isolation on the susceptible. Applied Mathematics Letters, 107, 106442, (2020).
• Bai, Y., Yao, L., Wei, T., Tian, F., Jin, D.Y., Chen, L. & Wang, M. Presumed Asymptomatic Carrier Transmission of COVID-19. JAMA, 323(14), 1406-1407, (2020).
• Sakurai, A., Sasaki, T., Kato, S., Hayashi, M., Tsuzuki, S.I., Ishihara, T., et al. Natural History of Asymptomatic SARS-CoV-2 Infection. N Engl J Med, 383(9), 885-886, (2020).
• Moore, S., Hill, E.M., Tildesley, M.J., Dyson, L., Keeling, M.J. Vaccination and non-pharmaceutical interventions for COVID-19: a mathematical modelling study. The Lancet Infectious Diseases, 21(6), 793-802, (2021).
• Aniţa, S., Banerjee, M., Ghosh, S., Volpert, V. Vaccination in a two-group epidemic model. Applied Mathematics Letters, 119, 107197, (2021).
• Estrada, E. COVID-19 and SARS-CoV-2: Modeling the present, looking at the future. Physics Reports, 869, 1-51, (2020).
• Bulai, I.M. Modeling Covid-19 Considering Asymptomatic Cases and Avoided Contacts. Chapter in Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells, Springer, (2021).
• https://www.istat.it/storage/rapporto-annuale/2018/Rapportoannuale2018.pdf.
• https://raw.githubusercontent.com/pcm-dpc/COVID-19/master/dati-json/dpc-covid19-ita-andamento-nazionale.json
• Pedersen, M.G., Meneghini, M. Quantifying undetected COVID-19 cases and effects of containment measures in Italy, (2020).
• National Institute of Infectious Diseases Japan. Field Briefing: Diamond Princess COVID-19 Cases, 20 Feb Update. Last accessed March 12, 2020. Available from: https://www.niid.go.jp/niid/en/2019-ncov-e/9417-covid-dp-fe-02.html.
• O. Diekmann, J.A.P. Heesterbeek, J.A.J. Metz. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. Journal of mathematical biology, 28, 365-382, (1990).
• P. Van den Driessche, J. Watmough. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci, 180(1), 29–48, (2002).