On an agent-based SIR model for multi-populations
DOI:
https://doi.org/10.5902/2179460X89848Keywords:
Saturated SIR model, Multi-Population dynamics, Diseases transmission, PredictionsAbstract
In this paper, we investigate the impact of epidemic spread in a SIR type model with saturation between multiple interacting populations. The model is derived from an average threshold that considers multiple agents. Theoretical analysis confirms the model's well-posedness, indicating that it possesses a unique solution that varies continuously on the basis of the initial conditions and parameters. Additionally, we conduct numerical simulations for a scenario involving two circulating strains, where we also explore the scenario in which the disease mutates upon transmission, leading to increased transmissibility. A comparison between the dynamics of the SIR model with and without saturation reveals that saturation results in a milder disease dynamics.
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References
Abbey, H. (1952). An examination of the reed-frost theory of epidemics. Hum. Biol., 24(3):201–233.
Allen, L. J. S. (2007). An introduction to Mathematical Biology. Pearson Prentice Hall.
Ascher, U. & Greif, C. (2011). A First Course in Numerical Methods. (1st ed). SIAM.
Dhaoui, I., Van Bortel, W., Arsevska, E., Hautefeuille, C., Alonso, S. T., & Kleef, E. (2022). Mathematical modelling of covid-19: a systematic review and quality assessment in the early epidemic response phase. International Journal of Infectious Diseases, 116:S110.
Hethcote, H. W. (2000). The mathematics of infectious diseases. SIAM Review, 42(4):599–653.
Kermack, W. & Mckendrick, A. (1927). A contribution to the mathematical theory of epidemics. The Royal Socity, 115(772):700–721.
Kolokolnikov, T. & Iron, D. (2021). Law of mass action and saturation in sir model with application to coronavirus modelling. Infectious Disease Modelling, 6(1):91–97.
Kutter, J. S., Spronken, M. I., Fraaij, P. L., Fouchier, R. A., & Herfst, S. (2018). Transmission routes of respiratory viruses among humans. Current Opinion in Virology, 28:142–151.
Lazo, M. J. & De Cezaro, A. (2021). Why can we observe a plateau even in an out of control epidemic outbreak? a seir model with the interaction of n distinct populations for covid-19 in brazil. Trends in Computational and Applied Mathematics, 22(1):109–123.
Marques, J. C., De Cezaro, A., & Lazo, M. J. (2022). A sir model with spatially distributed multiple populations interactions for disease dissemination. Trends in Computational and Applied Mathematics, 23(1):143–154.
Marques, J. C., De Cezaro, A., & Lazo, M. J. (2023). On an emerging plateau in a multi-population sir model. preprint, 23(1):1–21.
Maurmann, A. C., Travessini De Cezaro, F., & Cezaro, A. (2023). A fractional sirc model for the spread of diseases in two interacting populations. Latin-American Journal of Computing, 10(2):46–57.
Mistro, D. C. & Rodrigues, L. A. D. (2021). Impacto do distanciamento social em um modelo discreto para covid-19. Ciˆencia e Natura, 43(Ed. Esp.):e12.
Silva, M. I., Marques, J. C., Conza, A. O., De Cezaro, A., & Gomes, A. C. F. N. (2023). The stiffness phenomena for the epidemiological sir model: a numerical approach. Latin-American Journal of Computing, 10(2):32–45.
Sotomayor, J. (1979). Lic¸ ˜oes de Equac¸ ˜oes Diferenciais Ordin´arias. (11th vol). Instituto de Matem´atica Pura e Aplicada, CNPq.
Techl, G. (2012). Ordinary Differential Equations and Dynamical Systems. (140th vol, Graduate Studies in Mathematics). AMS.
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