#### An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2

Yıl: 2021 Cilt: 50 Sayı: 5 Sayfa Aralığı: 1548 - 1559 Metin Dili: İngilizce DOI: 10.15672/hujms.751734 İndeks Tarihi: 29-07-2022

An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2

Öz: It is important to recognize that the dynamics of each country are different. Therefore, the SARS-CoV-2 (COVID-19) pandemic necessitates each country to act locally, but keep thinking globally. Governments have a responsibility to manage their limited resources optimally while struggling with this pandemic. Managing the trade-offs regarding these dynamics requires some sophisticated models. ``Agent-based simulation'' is a powerful tool to create such kind of models. Correspondingly, this study addresses the spread of COVID-19 employing an interaction-oriented multi-agent SIR (Susceptible-Infected-Recovered) model. This model is based on the scale-free networks (incorporating (10,000) nodes) and it runs some experimental scenarios to analyze the main effects and the interactions of ``average-node-degree'', ``initial-outbreak-size'', ``spread-chance'', ``recovery-chance'', and ``gain-resistance'' factors on ``average-duration (of the pandemic last)'', ``average-percentage of infected'', ``maximum-percentage of infected'', and ``the expected peak-time''. Obtained results from this work can assist determining the correct tactical responses of partial lockdown.

Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

- [1] K. Ameri and K.D. Cooper, A network-based compartmental model for the spread of whooping cough in Nebraska, in: AMIA Jt Summits Transl Sci Proc 2019, 388–397, 2019.
- [2] N. Anand, A. Sabarinath, S. Geetha and S. Somanath, Predicting the spread of COVID-19 using SIR model augmented to incorporate quarantine and testing, Trans. Indian Natl. Acad. Eng. 5 (2), 141-148, 2020.
- [3] C. Augusta, G.W. Taylor and R. Deardon, Dynamic contact networks of swine movement in Manitoba, Canada: Characterization and implications for infectious disease spread, Transbound Emerg Dis 66 (5), 1910-1919, 2019.
- [4] R. Aziza, A. Borgi, H. Zgaya and B. Guinhouya ,SimNCD: An agent-based formalism for the study of noncommunicable diseases, Eng. Appl. Artif. Intell. 52, 235-247, 2016.
- [5] H. Bulut, M. Golgeli and F.M. Atay, Modelling personal cautiousness during the COVID-19 pandemic: a case study for Turkey and Italy, Nonlinear Dyn., 1-13, Doi:10.1007/s11071-021-06320-7, 2021.
- [6] C. Castillo-Chavéz, Z. Feng and W. Huang, On the Computation of R0 and its Role on Global Stability, Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, The IMA Vol in Math Appl 125, 31-65, 2002.
- [7] I. Cooper, A. Mondal and C.G. Antonopoulos, A SIR model assumption for the spread of COVID-19 in different communities, Chaos, Solitons & Fractals 139, 110057, 1-14, 2020.
- [8] O. Diekmann, J. Heesterbeek and J. Metz, On the definition and the computation of the basic reproduction ratio in models for infectious diseases in heterogeneous populations, J. Math. Biol. 28 (4), 365-382, 1990.
- [9] K. Dietz, The incidence of infectious diseases under the influence of seasonal fluctuations, in: Berger, J., Bühler, W.J., Repges, R. and Tautu, P. (ed.) Mathematical Models in Medicine, Lecture Notes in Biomathematics, 1-15, Springer, Berlin, Heidelberg, 1976.
- [10] M. Dottori and G. Fabricius, SIR model on a dynamical network and the endemic state of an infectious disease, Phys. A 434, 25-35, 2015.
- [11] P.V.D. Driessche and J.Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (1-2), 29-48, 2002.
- [12] M. Fontana and P. Terna, From agent-based models to network analysis (and return): The policy-making perspective, Research Center in Behavioral, Complexity and Experimental Economics, Working Paper Series 7 (15), 1–19, 2015.
- [13] M. Golgeli and F.M. Atay, Analysis of an epidemic model for transmitted diseases in a group of adults and an extension to two age classes, Hacet. J. Math. Stat. 49 (3), 921-934, 2020.
- [14] Y. Huang, L. Yang, H. Dai, F. Tian and K. Chen, Epidemic situation and forecasting of COVID-19 in and outside China, Bull World Health Organ, Doi:10.2471/BLT.20.255158, 2020.
- [15] F. Hussain, A. Ramanathan, L.L. Pullum and S.K. Jha, EpiSpec: A formal specification language for parameterized agent-based models against epidemiological ground truth, in: 2014 IEEE 4th International Conference on Computational Advances in Bio and Medical Sciences (ICCABS), IEEE, Miami, FL, USA, 16, 2014.
- [16] W.O. Kermack and A.G. McKendrick, A contribution to the mathematical theory of epidemics, in: Proceedings of the Royal Society of London, Series A, Containing Papers of a Mathematical and Physical Character 115 (772), 700-721, 1927.
- [17] Y. Kubera, P. Mathieu and S. Picault, IODA: An interaction-oriented approach for multi-agent based simulations, Auton. Agents Multi-Agent Syst. 23 (3), 303-343, 2011.
- [18] L.L. Lima and A.P.F. Atman, Impact of mobility restriction in COVID-19 superspreading events using agent-based model, PLOS One 16 (3), e0248708, 1-17, 2021.
- [19] X. Liu, G.J.D. Hewings, S. Wang, M. Qin, X. Xiang, S. Zheng and X. Li, Modeling the situation of COVID-19 and the effects of different containment strategies in China with dynamic differential equations and parameters estimation, medRxiv, Doi:10.1101/2020.03.09.20033498, 2020.
- [20] W.P. London and J.A. Yorke, Recurrent outbreaks of measles, chickenpox and mumps. I. Seasonal variation in contact rates, Am. J. Epidemiol. 98 (6), 453-468, 1973.
- [21] J.D. Loyal and Y. Chen, Statistical network analysis: A review with applications to the coronavirus disease 2019 pandemic, Int. Stat. Rev. 88 (2), 419-440, 2020.
- [22] C. Moore, G.S. Cumming, J. Slingsby and J. Grewar, Tracking socioeconomic vulnerability using network analysis: Insights from an avian influenza outbreak in an ostrich production network, PLoS One 9 (1), e86973, 1-12, 2014.
- [23] J. Mossong, N. Hens, M. Jit, P. Beutels, K. Auranen, R. Mikolajczyk, M. Massari, S. Salmaso, G.S. Tomba, J. Wallinga, J. Heijne, M. Sadkowska-Todys, M. Rosinska and W.J. Edmunds, Social contacts and mixing patterns relevant to the spread of infectious diseases, PLOS Medicine 5 (3), e74, 0381-0391, 2008.
- [24] J. Parker and J.M. Epstein, A distributed platform for global-scale agent-based models of disease transmission, ACM Trans. Model. Comput. Simul. 22 (1), 1-25, 2011.
- [25] H.V.D. Parunak, R. Savit and R.L. Riolo, Agent-based modeling vs. equation-based modeling: A case study and users’ guide, in: in: Sichman, J.S., Conte, R. and Gilbert, N. (ed.) Multi-Agent Systems and Agent-Based Simulation, Lecture Notes in Computer Science, 10-25, Springer, Berlin, 1998.
- [26] I.B. Schwartz and H.L. Smith, Infinite subharmonic bifurcation in an SEIR epidemic model, J. Math. Biol. 18 (3), 233-253, 1983.
- [27] S.T.A. Shah, M. Mansoor, A.F. Mirza, M. Dilshad, M.I. Khan, R. Farwa, M.A. Khan, M. Bilal and H.M.N. Iqbal, Predicting COVID-19 spread in Pakistan using the SIR Model, J. Pure Appl. Microbiol. 14 (2), 1423-1430, 2020.
- [28] R.V. Solé and S. Valverde, Information Theory of Complex Networks: On Evolution and Architectural Constraints, in: Ben-Naim, E., Frauenfelder, H. and Toroczkai, Z. (ed.) Complex Networks, Lecture Notes in Physics 650, 189-207, 2004.
- [29] G. Sonnino, Dynamics of the COVID-19-Comparison between the theoretical predictions and real data, arXiv:2003.13540 [q-bio.PE].
- [30] F. Stonedahl and U. Wilensky, Netlogo Virus on a Network Model, Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL, 2008.

APA | Altun K, Altuntas S, Dereli T (2021). An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2. , 1548 - 1559. 10.15672/hujms.751734 |

Chicago | Altun Koray,Altuntas Serkan,Dereli Türkay An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2. (2021): 1548 - 1559. 10.15672/hujms.751734 |

MLA | Altun Koray,Altuntas Serkan,Dereli Türkay An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2. , 2021, ss.1548 - 1559. 10.15672/hujms.751734 |

AMA | Altun K,Altuntas S,Dereli T An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2. . 2021; 1548 - 1559. 10.15672/hujms.751734 |

Vancouver | Altun K,Altuntas S,Dereli T An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2. . 2021; 1548 - 1559. 10.15672/hujms.751734 |

IEEE | Altun K,Altuntas S,Dereli T "An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2." , ss.1548 - 1559, 2021. 10.15672/hujms.751734 |

ISNAD | Altun, Koray vd. "An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2". (2021), 1548-1559. https://doi.org/10.15672/hujms.751734 |

APA | Altun K, Altuntas S, Dereli T (2021). An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2. Hacettepe Journal of Mathematics and Statistics, 50(5), 1548 - 1559. 10.15672/hujms.751734 |

Chicago | Altun Koray,Altuntas Serkan,Dereli Türkay An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2. Hacettepe Journal of Mathematics and Statistics 50, no.5 (2021): 1548 - 1559. 10.15672/hujms.751734 |

MLA | Altun Koray,Altuntas Serkan,Dereli Türkay An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2. Hacettepe Journal of Mathematics and Statistics, vol.50, no.5, 2021, ss.1548 - 1559. 10.15672/hujms.751734 |

AMA | Altun K,Altuntas S,Dereli T An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2. Hacettepe Journal of Mathematics and Statistics. 2021; 50(5): 1548 - 1559. 10.15672/hujms.751734 |

Vancouver | Altun K,Altuntas S,Dereli T An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2. Hacettepe Journal of Mathematics and Statistics. 2021; 50(5): 1548 - 1559. 10.15672/hujms.751734 |

IEEE | Altun K,Altuntas S,Dereli T "An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2." Hacettepe Journal of Mathematics and Statistics, 50, ss.1548 - 1559, 2021. 10.15672/hujms.751734 |

ISNAD | Altun, Koray vd. "An interaction-oriented multi-agent SIR model to assess the spread of SARS-CoV-2". Hacettepe Journal of Mathematics and Statistics 50/5 (2021), 1548-1559. https://doi.org/10.15672/hujms.751734 |