Application of the individual-based model for the epidemic process modeling

Forecasting of epidemic processes makes it possible to develop and substantiate measures to prevent the spread of infectious diseases among the population as well as eliminate the negative consequences caused by epidemics. The paper deals with modeling the development of the epidemic process by means of an individual-based model. In these models, modeling is carried out using not an average group, but an individual level with consideration to the heterogeneity of the population by characteristics. Each individual can have three states: Susceptible (S), Infected (I), or Recovered (R). Transmission in a population occurs from individuals in state I to individuals in state S. After recovering, individuals I change state to R and become immune. Immunity wanes over time and individuals R revert to a susceptible state S. This paper is devoted to the development and software implementation of an algorithm for solving an individually oriented model, which helps to study the population dynamics of those groups. The results obtained for various model parameter values are presented. The results obtained using the individual-based simulation are compared with the results obtained by solving numerically the well-known SIRS model, which is a system of ordinary differential equations. As a further work, it is planned to modify the model by introducing additional groups of individuals while taking into account additional individual parameters (age, spatial coordinates, social contacts, etc.). To reduce the computation time in the study of the epidemic spread in large populations, algorithm parallelizing appears to be a prospective option.

1. Grishunina Yu.V., Kontarov N.A., Arkharova G.V., Yuminova N.V. Modeling of Epidemic Situation Taking into Account External risks. Epidemiologiya i vaktsinoprofilaktika = Epidemiology and Vaccinal Prevention. 2014;78(5):61–66. (In Russ.).

2. Hethcote H.W. The Mathematics of Infectious Diseases. SIAM Review. 2000;42(4):599–653. DOI:10.1137/S0036144500371907.

3. Sofonea M.T., Cauchemez S, Boëlle P.-Y. Epidemic models: why and how to use them. Anaesthesia Critical Care & Pain Medicine. 2022;41(2):101048. Available from: https://linkinghub.elsevier.com/retrieve/pii/S2352556822000297. DOI: 10.1016/j.accpm.2022.101048 (accessed on 30.03.2023).

4. Abou-Ismail A. Compartmental Models of the COVID-19 Pandemic for Physicians and Physician-Scientists. SN Comprehensive Clinical Medicine. 2020;2(7):852–858. DOI: 10.1007/s42399-020-00330-z.

5. Kermack W.O., McKendrick A.G. A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London. 1927;115(772):700–721. DOI: 10.1098/rspa.1927.0118.

6. Piccirillo V. Nonlinear control of infection spread based on a deterministic SEIR model. Chaos, Solitons & Fractals. 2021;149:111051. Available from: https://linkinghub.elsevier.com/retrieve/pii/S0960077921004057 (accessed on 30.03.2023).

7. Borisenko A.B., Borisenko A.A. Application of the SIR-Model for Epidemic Process Modeling. Polzunovskii al'manakh. 2022;1(4):51–53. (In Russ.)

8. Sorokin P.A. Klassifikatsiya metodov individuum-orientirovannogo modelirovaniya. Issledovano v Rossii. 2003;6:574–588. (In Russ.).

9. Nepomuceno E.G., Takahashi R.H.C., Aguirre L.A. Individual-Based Model (IBM): an Alternative Framework for Epidemiological Compartment Models. Brazilian Journal of Biometrics. 2016;34(1):133–162. (In Russ.).

10. Nepomuceno E.G., Resende D.F., Lacerda M.J. A Survey of the Individual-Based Model applied in Biomedical and Epidemiology. Journal of Biomedical Research and Reviews. 2019;1(1):11–24. DOI: 10.48550/arXiv.1902.02784.

11. Railsback S.F., Grimm V. Agent-Based and Individual-Based Modeling: A Practical Introduction. Princeton: Princeton University Press; 2019. 339 p.

12. Ferrer J., Prats C., López D. Individual-based Modelling: An Essential Tool for Microbiology. Journal of Biological Physics. 2008;34(1–2):19–37. DOI: 10.1007/s10867-008-9082-3.

13. DeAngelis D.L. Individual-based models and approaches in ecology: populations, communities and ecosystems. CRC Press; 2017. 545 p.

14. Hazelbag C.M., Dushoff J., Dominic E.M., Mthombothi Z.E., Delva W. Calibration of individual-based models to epidemiological data: A systematic review. PLOS Computational Biology. 2020;16(5):e1007893. Available from: https://dx.plos.org/10.1371/journal.pcbi.1007893. DOI: 10.1371/journal.pcbi.1007893 (accessed on 30.03.2023).

15. Ageeva A.F. Simulation of epidemics: agent-based approach. Modelirovaniye, optimizatsiya i informatsionnyye tekhnologii = Modeling, Optimization and Information Technology. 2020;8(3). Available from: https://moit.vivt.ru/wpcontent/uploads/2020/08/Ageeva_3_20_1.pdf. DOI: 10.26102/2310-6018/2020.30.3.030 (accessed on 30.03.2023). (In Russ.).

16. Galvão Filho A.R., Martins de Paula L.C., Coelho C.J., de Lima T.W., da Silva Soares A. CUDA parallel programming for simulation of epidemiological models based on individuals. Mathematical Methods in the Applied Sciences. 2016;39(3):405–411. DOI:10.1002/mma.3490.