Skip to main content
SpringerLink
Log in

A Novel Approach Infectious Disease Outbreak Through Grid-Based Model

  • Conference paper
  • First Online:
Proceedings of the Future Technologies Conference (FTC) 2021, Volume 2 (FTC 2021)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 359))

Included in the following conference series:

Abstract

Infectious diseases have been characterized by menacing people’s lives, since they have several side effects which can be modeled using mathematical models, allowing its most cases to be represented through differential equations (ODE), making it arduous to analyze in very particular aspects in a population, including the rate of reinfection, transmission factor, and level of the virus lethality. Beneath, we introduce an approach of a compartmental model which consists of replacing differential equations with an outlook, permitting the development of peculiarities regarding individuals. The model considers connectivity among individuals, defining which of them will be able to influence each other and which may not, providing for a local rule that defines the outcome of iteration among connected individuals. This article compares the SIR and SEIRS models for infectious disease outbreaks using the grid-based method. The results can help governments by taking isolation measures, protecting people by allowing them to effectively reduce the number of infected and controlling the epidemic situation faster.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 229.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 299.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. WHO timeline of whos response to COVID-19 (2020). https://www.who.int/news-room/detail/29-06-2020-covidtimeline

  2. van den Driessche, P.: Deterministic compartmental models: extensions of basic models. In: Brauer, F., van den Driessche, P., Wu, J. (eds.) Mathematical Epidemiology, vol. 1945, pp. 147–157. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78911-6_5

    Chapter  MATH  Google Scholar 

  3. Monteiro, L.H.A., et al.: Big cities: shelters for contagious diseases. Ecol. Model. 197, 258–262 (2006)

    Article  Google Scholar 

  4. Siettos, C.I., Russo, L.: Mathematical modeling of infectious disease dynamics. Virulence 4(4), 295–306 (2013)

    Article  Google Scholar 

  5. John Graunt on causes of death in the city of London. Popul. Dev. Rev. 35(2), 417–422 (2009). Bailey NJT

    Google Scholar 

  6. Bernoulli, D.: An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it. Rev. Med. Virol. 14(5), 275–288 (2004). Reprinted in Blower, S.

    Article  Google Scholar 

  7. Signes Pont, M.T., et al.: The susceptible-infectious model of disease expansion analyzed under the scope of connectivity and neighbors’ rules. In: Proceedings of the CSITA Conference, Computer Science & Information Technology (CS & IT), vol. 7, no. 1, pp. 1–10, January 2017

    Google Scholar 

  8. Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. 115, 700–721 (1927)

    MATH  Google Scholar 

  9. Isea, R., Lonngren, K.E.: On the mathematical interpretation of epidemics by Kermack and McKendrick. Gen. Math. Notes 19(2), 83–87 (2013)

    MathSciNet  Google Scholar 

  10. Miller, J.C.: Mathematical models of SIR disease spread with combined non-sexual and sexual transmission routes. Infect. Dis. Model. 2, 35–55 (2017)

    Google Scholar 

  11. Decreusefond, L., et al.: Large graph limit for an SIR process in random network with heterogeneous connectivity. Ann. Appl. Probab. 22(2), 541–575 (2012)

    Article  MathSciNet  Google Scholar 

  12. Signes Pont, M.T., et al.: The susceptible-infectious-recovered (SIR) model of disease expansion: a new approach. In: 17th Edition of the Mathematical Modelling in Engineering and Human Behavior Conference, July 2017

    Google Scholar 

  13. Hethcote, H.W., van den Driessche, P.: Two SIS epidemiologic models with delays. J. Math. Biol. 40(1), 3–26 (2000). https://doi.org/10.1007/s002850050003

    Article  MathSciNet  MATH  Google Scholar 

  14. Jianquan, L., Zhien, M.: Global analysis of SIS epidemic models with variable total population size. Math. Comput. Model. 39, 1231–1242 (2004)

    Article  MathSciNet  Google Scholar 

  15. Signes Pont, M.T., et al.: A discrete approach of the susceptible-infectious-susceptible (SIS) model of disease expansion. Int. J. Comput. 2 (2017)

    Google Scholar 

  16. Yukihiko, N., Toshikazu, K.: Global dynamics of a class of SEIRS epidemic models in a periodic environment. J. Math. Anal. Appl. 363, 230–237 (2010)

    Article  MathSciNet  Google Scholar 

  17. Shah, N.H., Gupta, J.: SEIR model and simulation for vector borne diseases. Appl. Math. 4, 13–17 (2013)

    Article  Google Scholar 

  18. Mishra, B.K., Pandey, S.K.: Dynamic model of worm propagation in computer network. Appl. Math. Model. 38, 2173–2179 (2014)

    Article  MathSciNet  Google Scholar 

  19. Eftimie, R., Gillard, J.J., Cantrell, D.A.: Mathematical models for immunology: current state of the art and future research directions. Bull. Math. Biol. 78(10), 2091–2134 (2016). https://doi.org/10.1007/s11538-016-0214-9

    Article  MathSciNet  MATH  Google Scholar 

  20. Hill, A.L.: Mathematical models of HIV latency. In: Silvestri, G., Lichterfeld, M. (eds.) HIV-1 Latency. CTMI, vol. 417, pp. 131–156. Springer, Cham (2017). https://doi.org/10.1007/82_2017_77

    Chapter  Google Scholar 

  21. Chavali, A., et al.: Characterizing emergent properties of immunological systems with multi-cellular rule-based computational modeling. Trends Immunol. 29(12), 589–599 (2008). https://doi.org/10.1016/j.it.2008.08.006

    Article  Google Scholar 

  22. Graw, F., et al.: Inferring viral dynamics in chronically HCV infected patients from the spatial distribution of infected hepatocytes. PLoS Comput. Biol. 10(11), e1003934 (2014). https://doi.org/10.1371/journal.pcbi.1003934

    Article  Google Scholar 

  23. Graw, F., Perelson, A.S.: Modeling viral spread. Ann. Rev. Virol. 3(1), 555–572 (2016). https://doi.org/10.1146/annurev-virology-110615-042249

    Article  Google Scholar 

  24. Tomasini, M.D., et al.: Modeling the dynamics and kinetics of HIV-1 Gag during viral assembly. PLoS ONE 13(4), e0196133 (2018). https://doi.org/10.1371/journal.pone.0196133

    Article  Google Scholar 

  25. Signes-Pont, M.T., et al.: Modelling the malware propagation in mobile computer devices. Comput. Secur. 79, 80–93 (2018)

    Article  Google Scholar 

  26. Peng, S., et al.: Modeling the dynamics of worm propagation using two-dimensional cellular automata in smartphones. J. Comput. Syst. Sci. 79, 586–595 (2013)

    Article  MathSciNet  Google Scholar 

  27. Martín, Á., del Rey, G., Sánchez, R.: A CA Model for Mobile Malware Spreading Based on Bluetooth Connections. In: Herrero, Á., et al. (eds.) International Joint Conference SOCO’13-CISIS’13-ICEUTE’13, pp. 619–629. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-01854-6_63

    Chapter  Google Scholar 

  28. García, G.G., et al.: Worm propagation modeling considering smartphones heterogeneity and people mobility. In: Proceedings of the 2017 International Conference on Applied Mathematics, Modeling and Simulation (AMMS 2017). Advances in Intelligent Systems Research, vol. 153 (2017)

    Google Scholar 

  29. Mickler, A.R., et al.: Modeling infectious diseases using global stochastic cellular automata. J. Biol. Systems 13(4), 421–439 (2005)

    Article  Google Scholar 

  30. Reed, C., et al.: Estimates of the prevalence of pandemic (H1N1) 2009, United States, April–July 2009. Emerg. Infect. Dis. 15(12), 2004 (2009)

    Article  Google Scholar 

  31. Isea, R., Lonngren, K.E.: Epidemic modeling using data from the 2001–2002 measles outbreak in Venezuela. Res. Rev. BioSci. 7(1), 15–18 (2013)

    Google Scholar 

  32. Moghadas, S., Gumel, A.B.: A mathematical study of a model for childhood diseases with nonpermanent immunity. J. Comput. Appl. Math. 157(2), 347–363 (2003)

    Article  MathSciNet  Google Scholar 

  33. De Arazoza, H., Lounes, R.: A non-linear model for a sexually transmitted disease with contact tracing. IMA J. Math. Appl. Med. Biol. 19, 221–234 (2002). https://doi.org/10.1093/imammb/19.3.221

    Article  MATH  Google Scholar 

  34. Galindo-Urribari, S., et al.: Las matemáticas de las epidemias: caso México 2009 y otros. CIENCIA ergo-sum 20(3), 238–246 (2014)

    Google Scholar 

  35. He, X., Jia, W.: Hexagonal structure for intelligent vision. In: Proceedings of ICICT (2005)

    Google Scholar 

  36. Kitchovitch, S., Liò, P.: Community structure in social networks: applications for epidemiological modelling. PLoS ONE 6(7), e22220 (2011)

    Article  Google Scholar 

  37. Sabater, A.F., et al.: Simulación de la propagación del malware: Modelos continuos vs. Modelos discretos. In: Actas de la XIII Reunión Española sobre Criptología y Seguridad de la Información RECSI 2014 (2014)

    Google Scholar 

  38. Karyotis, V., Kakalis, A., Papavassiliou, S.: Malware-propagative mobile ad hoc networks: asymptotic behavior analysis. J. Comput. Sci. Technol. 23(3), 389–399 (2008). https://doi.org/10.1007/s11390-008-9141-z

    Article  Google Scholar 

  39. White, S.H., et al.: Modelling epidemics using cellular automata. Appl. Math. Comput. 186(1), 193–202 (2007)

    MathSciNet  MATH  Google Scholar 

  40. Song, Y., Jiang, G.: Research of malware propagation in complex networks based on 1-D cellular automata. Acta Phys. Sin. 58(9), 5901–5908 (2009)

    Google Scholar 

  41. Daley, D.J., Gani, J.: Epidemic Modeling: An Introduction. Cambridge University Press, New York (2005)

    MATH  Google Scholar 

  42. Feng, Y., Lu, X.: Simulation analysis of the coronavirus disease 2019(COVID-19) spread based on system dynamics model. In: 2020 IEEE International Conference on Systems, Man, and Cybernetics (SMC), Toronto, ON, Canada, pp. 498–501 (2020). https://doi.org/10.1109/SMC42975.2020.9282928

  43. Mikler, A.R., Venkatachalam, S., Abbas, K.: Modeling Infectious diseases using global stochastic cellular automata. J. Biol. Syst. 13(04), 421–439 (2005). https://doi.org/10.1142/S0218339005001616

    Article  MATH  Google Scholar 

  44. Bacaër, N.: A Short History of Mathematical Population Dynamics. Springer, London (2011). ISBN: 978-0-85729-114-1. https://doi.org/10.1007/978-0-85729-115-8

    Book  MATH  Google Scholar 

  45. Lucas, J., Cortés, J.C., Luis, A.: Infectious disease expansion: a discrete approach to the Kermarck and McKendrick model. In: Modelling for Engineering & Human Behaviour. Instituto Universitario de Matemáticas Multidisciplinar, Universitat Politécnica de Valéncia, Valencia, Spain, pp. 307–311 (2017). ISBN: 978-84-697-8505-8

    Google Scholar 

  46. Ochoa, S.F., Singh, P., Bravo, J.: Ubiquitous Computing and Ambient Intelligence: 11th International Conference, UCAmI 2017. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67585-5

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Informática, Universidad de Panamá, Panama, Republic of Panama

    Antonio Cortés

  2. Departamento de Tecnología Informática y Computación, Universidad de Alicante, Alicante, Spain

    Maria Teresa Signes Pont

Authors
  1. Antonio Cortés
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maria Teresa Signes Pont
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antonio Cortés .

Editor information

Editors and Affiliations

  1. Faculty of Science and Engineering, Saga University, Saga, Japan

    Kohei Arai

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Cortés, A., Signes Pont, M.T. (2022). A Novel Approach Infectious Disease Outbreak Through Grid-Based Model. In: Arai, K. (eds) Proceedings of the Future Technologies Conference (FTC) 2021, Volume 2. FTC 2021. Lecture Notes in Networks and Systems, vol 359. Springer, Cham. https://doi.org/10.1007/978-3-030-89880-9_55

Download citation

Publish with us

Policies and ethics

Search

Navigation