Compartmental Models of the COVID-19 Pandemic: A Systematic Literature Review

Year 2023, Volume: 6 Issue: 2, 254 - 267, 31.12.2023

Deniz Yerinde , Merve Er

https://doi.org/10.55117/bufbd.1395736

Abstract

As COVID-19 rapidly spread all around the world, different methods have been proposed to explore the dynamics of the pandemic, understand the transmission mechanism, and assess the preventive measures. Mathematical models are frequently used worldwide to predict various parameters and develop effective policies for disease control. Compartmental models are the most popular mathematical models in epidemiology. These models divide the population into distinct groups (compartments) based on their status and describe the movement of an individual from one compartment to another. Various compartmental models and their variations have been developed to model the pandemic dynamics and measure the efficiency and necessity of different initiatives such as lockdowns, face masks, and vaccination. This paper provides a systematic literature review on different compartmental models proposed to model the COVID-19 pandemic. These models are discussed in detail based on the compartmental structure in the model, aim of the model, variables, and methodological approaches.

Keywords

Compartmental model, Coronavirus, COVID-19, Epidemic modelling

COVID-19 Pandemisinin Kompartman Modelleri: Sistematik Bir Literatür Taraması

Abstract

COVID-19 hızla tüm dünyada yayılırken, bu pandeminin çeşitli yönleriyle ilgili çok sayıda çalışma yayınlanmıştır. Pandeminin dinamiklerini araştırmak, bulaşma mekanizmasını anlamak ve önleyici tedbirleri değerlendirmek için farklı yöntemler önerilmiştir. Matematiksel modeller, enfeksiyonun seyri için çeşitli parametreleri tahmin etmek ve hastalık kontrolü için etkili politikalar geliştirmek için dünya çapında sıklıkla kullanılmaktadır. Kompartman modelleri epidemiyolojideki en popüler matematiksel modellerdir. Bu modeller, popülasyonu durumlarına göre ayrı gruplara (kompartman) böler ve bir bireyin bir kompartmandan diğerine hareketini tanımlar. Pandeminin dinamiklerini modellemek ve karantina, yüz maskeleri ve aşılama gibi farklı girişimlerin etkinliğini ve gerekliliğini ölçmek için çeşitli kompartman modelleri ve varyasyonları geliştirilmiştir. Bu makale, literatürde COVID-19 pandemisini modellemek için önerilen farklı kompartman modelleri üzerine sistematik bir literatür taraması sunmaktadır. Bu modeller, modeldeki kompartman yapısı, modelin amacı, değişkenler ve metodolojik yaklaşımlar temelinde ayrıntılı olarak ele alınmıştır.

Keywords

Kompartman modelleri, Koronavirüs, COVID-19, Salgın modelleme

References

• [1] J. Riou, and C. L. Althaus, “Pattern of early human-to-human transmission of Wuhan 2019 novel coronavirus (2019-nCoV), December 2019 to January 2020”, Euro Surveill, 25(4), 2020.
• [2] World Health Organization Web Page. (2023, January 6). https://covid19.who.int
• [3] X. Yu, L. Lu, J. Shen, J. Li, W. Xiao, and Y. Chen, “RLIM: a recursive and latent infection model for the prediction of US COVID-19 infections and turning points”, Nonlinear dynamics, 106, pp. 1397-1410, 2021.
• [4] H. Leite, I.R. Hodgkinson, and T. Gruber, “New development: ‘Healing at a distance’—telemedicine and COVID-19”, Public Money & Management, 40(6), pp. 483–485, 2020.
• [5] A. Hurajova, D. Kolllarova, and L. Juraj, “Trends in education during the pandemic: modern online technologies as a tool for the sustainability of university education in the field of media and communication studies”, Heliyon, 8(5), pp. 2405-8440, 2022.
• [6] C. S. M. Currie, J. W. Fowler, K. Kotiadis, T. Monks, B. S. Onggo, D. A. Robertson, and A. A. Tako, “How simulation modelling can help reduce the impact of COVID19”, Journal of Simulation, 14(2), pp. 83-97, 2020.
• [7] S. Khalilpourazari, and H.H. Doulabi, “Robust modelling and prediction of the COVID-19 pandemic in Canada”, International Journal of Production Research, 2021.
• [8] M. Liu, R. Thomadsen, and S. Yao, “Forecasting the spread of COVID-19 under different reopening strategies”, Scientific Reports, 10(2036), 2020.
• [9] S.S. Nadim, I. Ghosh, and J. Chattopadhyay, “Short-term predictions and prevention strategies for COVID-19: A model-based study”, Applied Mathematics and Computation. 404(126251), 2021.
• [10] F. Brauer, “Compartmental models in epidemiology. In Mathematical epidemiology”, Springer, Berlin, Heidelberg, pp. 19-79, 2008.
• [11] G. Massonis, J. R. Banga, and A. F. Villaverde, “Structural identifiability and observability of compartmental models of the COVID-19 pandemic” Annual reviews in control, 51, pp. 441–459, 2021. [12] D. Prodanov, “Comments on some analytical and numerical aspects of the SIR model”, Applied Mathematical Modelling, 95, 2021.
• [13] T. Verma, and A.K. Gupta, “Network synchronization, stability and rhythmic processes in a diffusive mean-field coupled SEIR model”, Communications in Nonlinear Science and Numerical Simulation, 10, 2021.
• [14] P.S. Desai, “News Sentiment Informed Time-series Analyzing AI (SITALA) to curb the spread of COVID-19 in Houston”, Expert Systems with Applications, 180, 2021.
• [15] X. X. Liu, S. J. Fong, N. Dey, R. G. Crespo, and E. Herrera-Viedma, “A new SEAIRD pandemic prediction model with clinical and epidemiological data analysis on COVID-19 outbreak”, Applied intelligence, 51(7), pp. 4162–4198, 2021.
• [16] A. Safarishahrbijari, T. Lawrence, R. Lomotey, J. Liu, C. Waldner, and N. Osgood, “Particle filtering in a SEIRV simulation model of H1N1 influenza”, 2015 Winter Simulation Conference (WSC), pp. 1240-1251, 2015.
• [17] C.B.A. Satrio, W. Darmawan, B.U. Nadia, and N. Hanafiah, “Time series analysis and forecasting of coronavirus disease in Indonesia using ARIMA model and PROPHET”, Procedia Computer Science, 179, pp. 524-532, 2021.
• [18] V. Vig, and A. Kaur, “Time series forecasting and mathematical modeling of COVID-19 pandemic in India: a developing country struggling to cope up”, International Journal of System Assurance Engineering and Management, 13(6), pp. 2920-2933, 2022.
• [19] H. Bilgil, “New grey forecasting model with its application and computer code”, AIMS Mathematics, 6(2), pp. 1497–1514, 2020.
• [20] A. Saxena, “Grey forecasting models based on internal optimization for Novel Corona virus (COVID-19)”, Applied Soft Computing, Vol. 111, 107735, 2021.
• [21] D.N. Vinod, and S.R.S. Prabaharan, “COVID-19-The Role of Artificial Intelligence, Machine Learning, and Deep Learning: A Newfangled”, Archives of Computational Methods in Engineering, 30(4), pp. 2667-2682, 2023.
• [22] A. Kumar, P.K. Gupta, and A. Srivastava, “A review of modern technologies for tackling COVID-19 pandemic”, Diabetes & Metabolic Syndrome: Clinical Research & Reviews, 14(4), pp. 569-573, 2020.
• [23] L. Kong, M. Duan, J. Shi, J. Hong, Z. Chang, and Z. Zhang, “Compartmental structures used in modelling COVID-19: a scoping review”, Infectious Diseases of Poverty, 11 (72), 2022.
• [24] H. Duan, and W. Nie, “A novel grey model based on Susceptible Infected Recovered Model: A case study of COVD-19”, Physica A: Statistical Mechanics and its Applications, Vol. 602, 127622, 2022.
• [25] S.N. Zisad, M.S. Hossain, M.S. Hossain, and K. Andersson, “An Integrated Neural Network and SEIR Model to Predict COVID-19”, Algorithms, 14(3), 94, 2021.
• [26] S. Mac, S. Mishra, R. Ximenes, K. Barrett, Y.A. Khan, D.M.J. Naimark, and B. Sander, “Modeling the coronavirus disease 2019 pandemic: A comprehensive guide of infectious disease and decision-analytic models”, Journal of clinical epidemiology, 132, pp. 133–141, 2021.
• [27] M. Small, and D. Cavanagh, “Modelling Strong Control Measures for Epidemic Propagation With Networks-A COVID-19 Case Study”, IEEE Access, 2020.
• [28] A. Kumar, T.-M. Choi, S.F. Wamba, S. Gupta, and K.H. Tan, “Infection vulnerability stratification risk modelling of COVID-19 data: a deterministic SEIR epidemic model analysis”, Annals of Operations Research, 2021.
• [29] D.T. Volpatto, A.C.M. Resende, L. dos Anjos, J.V.O. Silva, C.M. Dias, R.C. Almeida, and S.M.C. Malta, “A generalised SEIRD model with implicit social distancing mechanism: A Bayesian approach for the identification of the spread of COVID-19 with applications in Brazil and Rio de Janeiro state”, Journal of Simulation, 2021.
• [30] M. Kim, and F. Milner, “A mathematical model of epidemics with screening and variable infectivity”, Mathematical and Computer Modelling, 21(7), pp. 29–42, 1995.
• [31] W. O. Kermack, and A.G.A. McKendrick, “Contribution to the mathematical theory of epidemics”, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society, pp. 700–721, 1927.
• [32] L. Tang, Y. Zhou, L. Wang, S. Purkayastha, L. Zhang, J. He, F. Wang, and P. X. Song, “A Review of Multi-Compartment Infectious Disease Models”, International Statistical Review, 88(2), pp. 462–513, 2020.
• [33] S.B. Bastos, M.M. Morato, D.O. Cajuiro, and J.E. Normey-Rico, “The COVID-19 (SARS-CoV-2) uncertainty tripod in Brazil: Assessments on model-based predictions with large under-reporting”, Alexandria Engineering Journal, 60(5), pp. 4363-4380, 2021.
• [34] K. P. Ayodele, H. Jimoh, A. F. Fagbamigbe, and O. H. Onakpoya, “The dynamics of COVID-19 outbreak in Nigeria: A sub-national analysis”, Scientific African, 13, 2021.
• [35] N. Menon, “Does BMI predict the early spatial variation and intensity of Covid-19 in developing countries? Evidence from India”, Economics and Human Biology, 41, 2021.
• [36] E. Acosta-González, J. Andrada-Félix, and F. Fernández-Rodríguez, “On the evolution of the COVID-19 epidemiological parameters using only the series of deceased. A study of the Spanish outbreak using Genetic Algorithms”, Mathematics and computers in simulation, 197, pp. 91–104, 2022.
• [37] G. V. La, V. Moscato, M. Postiglione, and G. Sperli, “An epidemiological neural network exploiting dynamic graph structured data applied to the COVID-19 outbreak”, IEEE Transactions on Big Data, 7(1), pp. 45-55, 2021.
• [38] J. Rubio-Herrero, and Y. Wang, “A flexible rolling regression framework for the identification of time-varying SIRD models”, Computers and Industrial Engineering, 167, 2022.
• [39] G. Chowell, “Fitting dynamic models to epidemic outbreaks with quantified uncertainty: A primer for parameter uncertainty, identifiability, and forecasts”, Infectious Disease Modelling. 2. pp. 379– 398, 2017.
• [40] D. Vrabac, M. Shang, B. Butler, J. Pham, R. Stern, and P.E. Pare, “Capturing the Effects of Transportation on the Spread of COVID-19 with a Multi-Networked SEIR Model”, IEEE Control Systems Letters, 6, pp. 103-108, 2022.
• [41] C.C. John, V. Ponnusamy, C. S. Krishnan, and N. Ra, “A Survey on Mathematical, Machine Learning and Deep Learning Models for COVID-19 Transmission and Diagnosis”, IEEE Reviews in Biomedical Engineering, 5, pp. 325-340, 2022.
• [42] T. Pechlivanoglou, J. Li, J. Sun, F. Heidari, and M. Papagelis, “Epidemic Spreading in Trajectory Networks”, Big Data Research, 27, 2022.
• [43] Z. Ma, S. Wang, X. Lin, X. Li, X. Han, H. Wang, and H. Liu, “Modeling for COVID-19 with the contacting distance”, Nonlinear Dynamics, 107(3), pp. 3065-3084, 2022.
• [44] H. Alrabaiah, M. Arfan, K. Shah, I. Mahariq, and A. Ullah, “A comparative study of spreading of novel corona virus disease by ussing fractional order modified SEIR model”, Alexandria Engineering Journal, 60(1), pp. 573-585, 2021.
• [45] D. Majumder, S. Mazumder, and P. Ghosal, “CARD Predictive Modeling and SEI Formulation: COVID-19 Statistics in India”, Journal of The Institution of Engineers (India): Series B, 102(6), pp. 1167–1176, 2021.
• [46] Y. Li, Z. Zeng, M. Feng, and J. Kurths, “Protection Degree and Migration in the Stochastic SIRS Model: A Queueing System Perspective”, IEEE Transactions on Circuits and Systems I: Regular Papers, 69(2), pp. 771-783, 2022.
• [47] I.N. Lymperopoulos, “#stayhome to contain Covid-19: Neuro-SIR – Neurodynamical epidemic modeling of infection patterns in social networks”, Expert Systems with Applications, 165, 2021.
• [48] D. Chen, Y. Yang, Y. Zhang, and W. Yu, “Prediction of COVID-19 spread by sliding mSEIR observer”, Science China Information Sciences, 63(12), 2020.
• [49] X. Meng, Z. Cai, S. Si, and D. Duan, “Analysis of epidemic vaccination strategies on heterogeneous networks: Based on SEIRV model and evolutionary game”, Applied mathematics and computation, 403, 2021.
• [50] A. Carpio, and Pierret, E. “Uncertainty quantification in Covid-19 spread: Lockdown effects”, Results in physics, 35, 2022.
• [51] C.T. Deressa, and G.F. Duressa, “Investigation of the dynamics of COVID-19 with SEIHR nonsingular and nonlocal kernel fractional model”, International Journal of Modelling and Simulation, 2021.
• [52] P. Kumari, H. P. Singh, and S. Singh, “SEIAQRDT model for the spread of novel coronavirus (COVID-19): A case study in India”, Applied intelligence (Dordrecht, Netherlands), 51(5), pp. 2818–2837, 2021.
• [53] M. A. Bahloul, A. Chahid, and T. M. Laleg-Kirati, “Fractional-Order SEIQRDP Model for Simulating the Dynamics of COVID-19 Epidemic”, IEEE open journal of engineering in medicine and biology, 1, 249–256, 2020.
• [54] H. Hethcote, “The Mathematics of Infectious Diseases”, SIAM Review, 42 (4), pp. 599–653, 2000.
• [55] D. Guanghong, L. Chang, G. Jianqiu, W. Ling, C. Ke, and Z. Di, “SARS epidemical forecast research in mathematical model”. Chin Sci Bull, 49(21), pp. 2332-2338, 2004.
• [56] R.C. Poonia, A.K.J. Saudagar, A. Altameem, M. Alkhathami, M.B. Khan, and M.H.A. Hasanat, “An Enhanced SEIR Model for Prediction of COVID-19 with Vaccination Effect”, Life, 12, 647, 2022.
• [57] R.N.U. Rajapaksha, M.S.D. Wijesinghe, S.P. Jayasooriya, B.I. Gunawardana, and W.P.C. Weerasinghe, “An Extended Susceptible Exposed-Infected-Recovered (SEIR) Model with Vaccination for Forecasting the COVID-19 Pandemic in Sri Lanka”, medRxiz&bioRxiv, 2021.
• [58] S. Magesh, V.R. Niveditha, P.S. Rajakumar, S. Radha RamMohan, and L. Natrayan, “Pervasive computing in the context of COVID-19 prediction with AI-based algorithms”, International Journal of Pervasive Computing and Communications, 16(5), pp. 477-487, 2020.
• [59] W. Qian, S. Bhowmick, M. Neill, S.R. Mikler, and A.R. Mikler, “Applying a Probabilistic Infection Model for studying contagion processes in contact networks”, Journal of Computational Science, 54, 2021.
• [60] K. Roosa, and G. Chowell, “Assessing parameter identifiability in compartmental dynamic models using a computational approach: application to infectious disease transmission models”, Theoretical biology & medical modelling, 16(1), 2019.
• [61] W. C. Roda, M. B. Varughese, D. Han, and M. Y. Li, “Why is it difficult to accurately predict the COVID-19 epidemic?”, Infectious Disease Modelling, 5, pp. 271–281, 2020.
• [62] Y. Wu, Y. Sun, and M. Lin, “SQEIR: An epidemic virus spread analysis and prediction model”, Computers and Electrical Engineering, 102, 108230, 2022.
• [63] M. Fošnarič, T. Kamenšek, and J. Žganec Gros, et al. “Extended compartmental model for modeling COVID-19 epidemic in Slovenia”, Scientific Reports, 12, 16916, 2022.
• [64] X. Lu, and E. Borgonovo, “Global sensitivity analysis in epidemiological modelling”, European journal of operational research, 304(1), pp. 9–24, 2023.
• [65] K. Chen, C. S. Pun, and H. Y. Wong, “Efficient Social Distancing during the COVID-19 Pandemic: Integrating Economic and Public Health Considerations”, European journal of operational research, 304(1), pp. 84-98, 2023.
• [66] M. Rafiq, A.R. Nizami, D. Baleanu, and N. Ahmad, “Numerical simulations on scale-free and random networks for the spread of COVID-19 in Pakistan”, Alexandria Engineering Journal, 62, pp. 75-83, 2023.
• [67] C. Durai, A. Begum, J. Jebaseeli, and A. Sabahath, “COVID-19 pandemic, predictions and control in Saudi Arabia using SIR-F and age-structured SEIR model”, The Journal of supercomputing, 78(5), pp. 7341–7353, 2022.
• [68] W. H. Chiang, X. Liu, and G. Mohler, “Hawkes process modeling of COVID-19 with mobility leading indicators and spatial covariates”, International journal of forecasting, 38(2), pp. 505–520, 2022.
• [69] H. Yuan, J. Shi, J. Wang, and W. Liu “Modelling network public opinion polarization based on SIR model considering dynamic network structure”, Alexandria Engineering Journal, 61(6), pp. 4557-4571, 2022.
• [70] B. Alsinglawi, O. Mubin, F. Alnajjar, K. Kheirallah, M. Elkhodr, M. Al Zobbi, M. Novoa, M. Arsalan, T. N. Poly, M. Gochoo, G. Khan, and K. Dev, “A simulated measurement for COVID-19 pandemic using the effective reproductive number on an empirical portion of population: epidemiological models”, Neural computing & applications, pp. 1–9, 2021.
• [71] A. Kuzdeuov, A. Karabay, D. Baimukashev, B. Ibragimov, and H. A. Varol, “A Particle-Based COVID-19 Simulator With Contact Tracing and Testing”, Journal of engineering in medicine and biology, 2, pp. 111–117, 2021.
• [72] L. Aggarwal, P. Goswami, and S. Sachdeva, “Multi-criterion Intelligent Decision Support system for COVID-19”, Applied soft computing, 101, 2021.
• [73] P. Yarsky, “Using a genetic algorithm to fit parameters of a COVID-19 SEIR model for US states”, Mathematics and computers in simulation, 185, pp. 687–695, 2021.
• [74] P. Mellacher, “Endogenous viral mutations, evolutionary selection, and containment policy design”, Journal of economic interaction and coordination, 17(3), pp. 801–825, 2022.
• [75] H.X. Huynh, B.U. Lai, N. Duong-Trung, H.T. Nguyen, and T.C. Phan, “Modeling population dynamics for information dissemination through Facebook”, Concurrency Computation Practise and Experience, 2021.
• [76] M. Abdy, S. Side, S. Annas, W. Nur, and W. Sanusi, “An SIR epidemic model for COVID-19 spread with fuzzy parameter: the case of Indonesia”, Advances in difference equations, 2021(1), 105, 2021.
• [77] C. Gourieroux, and J. Jasiak, “Time varying Markov process with partially observed aggregate data: An application to coronavirus”, Journal of econometrics, 232(1), pp. 35–51, 2023.
• [78] A. Kumar, B. Priya, and S.K. Srivasta, “Response to the COVID-19: Understanding implications of government lockdown policies”, Journal of Policy Modeling, 43(1), pp. 76-94, 2021.
• [79] M. Gillis, R. Urban, A. Saif, N. Kamal, and M. Murphy, “A simulation–optimization framework for optimizing response strategies to epidemics”, Operations Research Perspectives, 8, 2021.
• [80] R. Carli, G. Cavone, N. Epicoco, P. Scarabaggio, and M. Dotoli, “Model predictive control to mitigate the COVID-19 outbreak in a multi-region scenario”, Annual reviews in control, 50, pp. 373–393, 2020.
• [81] H. Garg, A. Nasir, N. Jan, and S. U. Khan, “Mathematical analysis of COVID-19 pandemic by using the concept of SIR model”, Soft computing, 2021.
• [82] J. Bradley, A. Ruggieri, and A.H. Spencer, “Twin Peaks: Covid-19 and the labor market”, European Economic Review, 138, 2021.
• [83] Y. Iwamoto, “Welfare economics of managing an epidemic: an exposition”, Japanese economic review (Oxford, England), 72(4), pp. 537–579, 2021.
• [84] H. Bilgil, A. Yousef, A. Erciyes, Ü. Erdinç, and Z. Öztürk, “A fractional-order mathematical model based on vaccinated and infected compartments of SARS-CoV-2 with a real case study during the last stages of the epidemiological event”, Journal of computational and applied mathematics, 425, 115015, 2023.
• [85] A. Spannaus, T. Papamarkou, S. Erwin, and J. B. Christian, “Inferring the spread of COVID-19: the role of time-varying reporting rate in epidemiological modelling”, Scientific reports, 12(1), 10761, 2022.
• [86] M. Khairulbahri, “Lessons learned from three Southeast Asian countries during the COVID-19 pandemic”, Journal of policy modeling, 43(6), pp. 1354–1364, 2021.
• [87] N. Gatti, and B. Retali, “Saving lives during the COVID-19 pandemic: the benefits of the first Swiss lockdown”, Swiss journal of economics and statistics, 157(1), 4, 2021.