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06-06-2022 | Regular Paper

Exo-SIR: an epidemiological model to analyze the impact of exogenous spread of infection

Authors: Nirmal Kumar Sivaraman, Manas Gaur, Shivansh Baijal, Sakthi Balan Muthiah, Amit Sheth

Published in: International Journal of Data Science and Analytics

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Abstract

Epidemics like Covid-19 and Ebola have impacted people’s lives significantly. The impact of mobility of people across the countries or states in the spread of epidemics has been significant. The spread of disease due to factors local to the population under consideration is termed the endogenous spread. The spread due to external factors like migration, mobility, etc., is called the exogenous spread. In this paper, we introduce the Exo-SIR model, an extension of the popular SIR model and a few variants of the model. The novelty in our model is that it captures both the exogenous and endogenous spread of the virus. First, we present an analytical study. Second, we simulate the Exo-SIR model with and without assuming contact network for the population. Third, we implement the Exo-SIR model on real datasets regarding Covid-19 and Ebola. We found that endogenous infection is influenced by exogenous infection. Furthermore, we found that the Exo-SIR model predicts the peak time better than the SIR model. Hence, the Exo-SIR model would be helpful for governments to plan policy interventions at the time of a pandemic.
Literature
1.
go back to reference Harko, T., Lobo, F.S., Mak, M.: Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates. Appl. Math. Comput. 236, 184–194 (2014) MathSciNetMATH Harko, T., Lobo, F.S., Mak, M.: Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates. Appl. Math. Comput. 236, 184–194 (2014) MathSciNetMATH
3.
go back to reference Kumar, A., Gupta, P.K., Srivastava, A.: A review of modern technologies for tackling COVID-19 pandemic. Diabetes Metab. Syndr. Clin. Res. Rev. 14(4), 569–573 (2020) CrossRef Kumar, A., Gupta, P.K., Srivastava, A.: A review of modern technologies for tackling COVID-19 pandemic. Diabetes Metab. Syndr. Clin. Res. Rev. 14(4), 569–573 (2020) CrossRef
4.
go back to reference Kotwal, A., Yadav, A.K., Yadav, J., Kotwal, J., Khune, S.: Predictive models of COVID-19 in India: a rapid review. Med. J. Armed Forces India 76(4), 377–386 (2020) CrossRef Kotwal, A., Yadav, A.K., Yadav, J., Kotwal, J., Khune, S.: Predictive models of COVID-19 in India: a rapid review. Med. J. Armed Forces India 76(4), 377–386 (2020) CrossRef
6.
go back to reference Asawa, P., Gaur, M., Roy, K., Sheth, A.: COVID-19 in Spain and India: comparing policy implications by analyzing epidemiological and social media data. arXiv preprint arXiv:​2010.​14628 (2020) Asawa, P., Gaur, M., Roy, K., Sheth, A.: COVID-19 in Spain and India: comparing policy implications by analyzing epidemiological and social media data. arXiv preprint arXiv:​2010.​14628 (2020)
7.
go back to reference Rajan, S.I., Sivakumar, P., Srinivasan, A.: The COVID-19 pandemic and internal labour migration in India: a ‘crisis of mobility’. Indian J. Labour Econ. 63(4), 1021–1039 (2020) CrossRef Rajan, S.I., Sivakumar, P., Srinivasan, A.: The COVID-19 pandemic and internal labour migration in India: a ‘crisis of mobility’. Indian J. Labour Econ. 63(4), 1021–1039 (2020) CrossRef
8.
go back to reference Roy, K., Zhang, Q., Gaur, M., Sheth, A.: Knowledge infused policy gradients with upper confidence bound for relational bandits. In: Oliver, N., Pérez-Cruz, F., Kramer, S., Read, J., Lozano, J.A. (Eds.) Joint European Conference on Machine Learning and Knowledge Discovery in Databases, pp. 35–50. Springer, Cham (2021) Roy, K., Zhang, Q., Gaur, M., Sheth, A.: Knowledge infused policy gradients with upper confidence bound for relational bandits. In: Oliver, N., Pérez-Cruz, F., Kramer, S., Read, J., Lozano, J.A. (Eds.) Joint European Conference on Machine Learning and Knowledge Discovery in Databases, pp. 35–50. Springer, Cham (2021)
9.
10.
go back to reference Gaur, M., Kursuncu, U., Sheth, A., Wickramarachchi, R., Yadav, S.: Knowledge-infused deep learning. In: Proceedings of the 31st ACM Conference on Hypertext and Social Media, pp. 309–310 (2020) Gaur, M., Kursuncu, U., Sheth, A., Wickramarachchi, R., Yadav, S.: Knowledge-infused deep learning. In: Proceedings of the 31st ACM Conference on Hypertext and Social Media, pp. 309–310 (2020)
11.
go back to reference Zhou, G., Sun, L., Xia, R., Duan, Y., Xu, J., Yang, H., Wang, Y., Lee, M.C., Xiang, Z., Yan, G., et al.: Clinical malaria along the China-Myanmar border, Yunnan Province, China, January 2011-August 2012. Emerg. Infect. Dis. 20(4), 675 (2014) CrossRef Zhou, G., Sun, L., Xia, R., Duan, Y., Xu, J., Yang, H., Wang, Y., Lee, M.C., Xiang, Z., Yan, G., et al.: Clinical malaria along the China-Myanmar border, Yunnan Province, China, January 2011-August 2012. Emerg. Infect. Dis. 20(4), 675 (2014) CrossRef
12.
go back to reference Brauer, F., Castillo-Chavez, C.: Mathematical Models in Population Biology and Epidemiology. Texts in Applied Mathematics. Springer, New York (2011) Brauer, F., Castillo-Chavez, C.: Mathematical Models in Population Biology and Epidemiology. Texts in Applied Mathematics. Springer, New York (2011)
13.
go back to reference Tolles, J., Luong, T.: Modeling epidemics with compartmental models. Jama 323(24), 2515–2516 (2020) CrossRef Tolles, J., Luong, T.: Modeling epidemics with compartmental models. Jama 323(24), 2515–2516 (2020) CrossRef
14.
go back to reference Walker, P.G., Whittaker, C., Watson, O.J., Baguelin, M., Winskill, P., Hamlet, A., Djafaara, B.A., Cucunubá, Z., Olivera Mesa, D., Green, W., et al.: The impact of COVID-19 and strategies for mitigation and suppression in low-and middle-income countries. Science 369(6502), 413–422 (2020) MathSciNetCrossRef Walker, P.G., Whittaker, C., Watson, O.J., Baguelin, M., Winskill, P., Hamlet, A., Djafaara, B.A., Cucunubá, Z., Olivera Mesa, D., Green, W., et al.: The impact of COVID-19 and strategies for mitigation and suppression in low-and middle-income countries. Science 369(6502), 413–422 (2020) MathSciNetCrossRef
15.
go back to reference Goel, R., Bonnetain, L., Sharma, R., Furno, A.: Mobility-based SIR model for complex networks: with case study of COVID-19. Soc. Netw. Anal. Min. 11(1), 1–18 (2021) Goel, R., Bonnetain, L., Sharma, R., Furno, A.: Mobility-based SIR model for complex networks: with case study of COVID-19. Soc. Netw. Anal. Min. 11(1), 1–18 (2021)
16.
go back to reference Kumar, P., Sinha, A.: Information diffusion modeling and analysis for socially interacting networks. Soc. Netw. Anal. Min. 11(1), 1–18 (2021) CrossRef Kumar, P., Sinha, A.: Information diffusion modeling and analysis for socially interacting networks. Soc. Netw. Anal. Min. 11(1), 1–18 (2021) CrossRef
17.
go back to reference Myers, S.A., Zhu, C., Leskovec, J.: Information diffusion and external influence in networks. In: Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 33–41 (2012) Myers, S.A., Zhu, C., Leskovec, J.: Information diffusion and external influence in networks. In: Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 33–41 (2012)
18.
go back to reference Li, J., Xiong, J., Wang, X.: Measuring the external influence in information diffusion. In: 2015 16th IEEE International Conference on Mobile Data Management. IEEE vol. 2, pp. 92–97 (2015) Li, J., Xiong, J., Wang, X.: Measuring the external influence in information diffusion. In: 2015 16th IEEE International Conference on Mobile Data Management. IEEE vol. 2, pp. 92–97 (2015)
19.
go back to reference Yang, D., Liao, X., Wei, J., Chen, G., Cheng, X.: Modeling information diffusion with the external environment in social networks. J. Internet Technol. 20(2), 369–377 (2019) Yang, D., Liao, X., Wei, J., Chen, G., Cheng, X.: Modeling information diffusion with the external environment in social networks. J. Internet Technol. 20(2), 369–377 (2019)
20.
go back to reference De, A., Bhattacharya, S., Ganguly, N.: Demarcating endogenous and exogenous opinion diffusion process on social networks. In: Proceedings of the 2018 World Wide Web Conference, pp. 549–558 (2018) De, A., Bhattacharya, S., Ganguly, N.: Demarcating endogenous and exogenous opinion diffusion process on social networks. In: Proceedings of the 2018 World Wide Web Conference, pp. 549–558 (2018)
21.
go back to reference Fujita, K., Medvedev, A., Koyama, S., Lambiotte, R., Shinomoto, S.: Identifying exogenous and endogenous activity in social media. Phys. Rev. E 98(5), 052304 (2018) CrossRef Fujita, K., Medvedev, A., Koyama, S., Lambiotte, R., Shinomoto, S.: Identifying exogenous and endogenous activity in social media. Phys. Rev. E 98(5), 052304 (2018) CrossRef
22.
go back to reference Agrawal, R., Potamias, M., Terzi, E.: Learning the nature of information in social networks. In: Sixth International AAAI Conference on Weblogs and Social Media (2012) Agrawal, R., Potamias, M., Terzi, E.: Learning the nature of information in social networks. In: Sixth International AAAI Conference on Weblogs and Social Media (2012)
23.
go back to reference Oka, M., Hashimoto, Y., Ikegami, T.: Self-organization on social media: Endo-Exo bursts and baseline fluctuations. PLoS One 9(10), 109293 (2014) CrossRef Oka, M., Hashimoto, Y., Ikegami, T.: Self-organization on social media: Endo-Exo bursts and baseline fluctuations. PLoS One 9(10), 109293 (2014) CrossRef
24.
go back to reference Crane, R., Sornette, D.: Robust dynamic classes revealed by measuring the response function of a social system. Proc. Natl. Acad. Sci. 105(41), 15649–15653 (2008) CrossRef Crane, R., Sornette, D.: Robust dynamic classes revealed by measuring the response function of a social system. Proc. Natl. Acad. Sci. 105(41), 15649–15653 (2008) CrossRef
26.
go back to reference Dandekar, R., Rackauckas, C., Barbastathis, G.: A machine learning-aided global diagnostic and comparative tool to assess effect of quarantine control in COVID-19 spread. Patterns 1(9), 100145 (2020) CrossRef Dandekar, R., Rackauckas, C., Barbastathis, G.: A machine learning-aided global diagnostic and comparative tool to assess effect of quarantine control in COVID-19 spread. Patterns 1(9), 100145 (2020) CrossRef
28.
go back to reference Kaxiras, E., Neofotistos, G.: Multiple epidemic wave model of the COVID-19 pandemic: modeling study. J. Med. Internet Res. 22(7), 20912 (2020) CrossRef Kaxiras, E., Neofotistos, G.: Multiple epidemic wave model of the COVID-19 pandemic: modeling study. J. Med. Internet Res. 22(7), 20912 (2020) CrossRef
29.
go back to reference Chen, Y.-C., Lu, P.-E., Chang, C.-S., Liu, T.-H.: A time-dependent SIR model for COVID-19 with undetectable infected persons. IEEE Trans. Netw. Sci. Eng. 7(4), 3279–3294 (2020) MathSciNetCrossRef Chen, Y.-C., Lu, P.-E., Chang, C.-S., Liu, T.-H.: A time-dependent SIR model for COVID-19 with undetectable infected persons. IEEE Trans. Netw. Sci. Eng. 7(4), 3279–3294 (2020) MathSciNetCrossRef
30.
go back to reference Jung, S.Y., Jo, H., Son, H., Hwang, H.J.: Real-world implications of a rapidly responsive COVID-19 spread model with time-dependent parameters via deep learning: Model development and validation. J. Med. Internet Res. 22(9), 19907 (2020) CrossRef Jung, S.Y., Jo, H., Son, H., Hwang, H.J.: Real-world implications of a rapidly responsive COVID-19 spread model with time-dependent parameters via deep learning: Model development and validation. J. Med. Internet Res. 22(9), 19907 (2020) CrossRef
31.
go back to reference Radcliffe, J.: The mathematical theory of infectious diseases and its applications. J. R. Stat. Soc. Ser. C (Appl. Stat.) 26(1), 85–87 (1977) Radcliffe, J.: The mathematical theory of infectious diseases and its applications. J. R. Stat. Soc. Ser. C (Appl. Stat.) 26(1), 85–87 (1977)
34.
go back to reference Barabási, A.-L.: Network science. Philos. Trans. R. Soci. A Math. Phys. Eng. Sci. 371(1987), 20120375 (2013) CrossRef Barabási, A.-L.: Network science. Philos. Trans. R. Soci. A Math. Phys. Eng. Sci. 371(1987), 20120375 (2013) CrossRef
Metadata
Title
Exo-SIR: an epidemiological model to analyze the impact of exogenous spread of infection
Authors
Nirmal Kumar Sivaraman
Manas Gaur
Shivansh Baijal
Sakthi Balan Muthiah
Amit Sheth
Publication date
06-06-2022
Publisher
Springer International Publishing
Published in
International Journal of Data Science and Analytics
Print ISSN: 2364-415X
Electronic ISSN: 2364-4168
DOI
https://doi.org/10.1007/s41060-022-00334-z

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