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Diffusion model for the spread of infectious diseases: SIR model with mobile agents

Author

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  • Centres, P.M.
  • Perez-Morelo, D.J.
  • Guzman, R.
  • Reinaudi, L.
  • Gimenez, M.C.

Abstract

Using a model of agent diffusion over a square region and based on the SIR model, we perform a phenomenological study of the spread of an epidemic, considering two possible contagion mechanisms, namely (i) on the one hand, if a susceptible agent is on contact with an infected agent, it would become an infected agent with a given probability p1; (ii) on the other hand, if a group of susceptible agents is located within a cut-off radius Rc around an infected one, each of the susceptible agents would become an infected agent with probability p2. It was observed that the number of secondary infections produced by an individual during its infectious period, R0, has a dependence on p1, p2, Rc, the speed of the agents and the time of infection.

Suggested Citation

  • Centres, P.M. & Perez-Morelo, D.J. & Guzman, R. & Reinaudi, L. & Gimenez, M.C., 2024. "Diffusion model for the spread of infectious diseases: SIR model with mobile agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    • Handle: RePEc:eee:phsmap:v:633:y:2024:i:c:s0378437123009548
    DOI: 10.1016/j.physa.2023.129399
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    References listed on IDEAS

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    1. Yang, Han-Xin & Tang, Ming & Wang, Zhen, 2018. "Suppressing epidemic spreading by risk-averse migration in dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 347-352.
    2. Aiello, O.E. & da Silva, M.A.A., 2003. "New approach to dynamical Monte Carlo methods: application to an epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 327(3), pages 525-534.
    3. Carol Y. Lin, 2008. "Modeling Infectious Diseases in Humans and Animals by KEELING, M. J. and ROHANI, P," Biometrics, The International Biometric Society, vol. 64(3), pages 993-993, September.
    4. Fabricius, Gabriel & Maltz, Alberto, 2020. "Exploring the threshold of epidemic spreading for a stochastic SIR model with local and global contacts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    5. Aièllo, O.E & Haas, V.J & daSilva, M.A.A & Caliri, A, 2000. "Solution of deterministic–stochastic epidemic models by dynamical Monte Carlo method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(3), pages 546-558.
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    1. Zou, Hao & Sheng, Dian & Jiang, Jiehui, 2024. "Impact of trans-regional travel-related testing on epidemic spreading," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 643(C).
    2. Marcolongo, Benjamín & Peruani, Fernando & Sibona, Gustavo J., 2024. "Assessing the forecasting power of mean-field approaches for disease spreading using active systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 648(C).
    3. He, Yongming & Jin, Yufeng & Cao, Jian & Sui, Shengchun & Wang, Jiahe & Ran, Bin, 2025. "Identification of key nodes in urban bus-metro network: A NK-shell algorithm based neighborhood KS," Reliability Engineering and System Safety, Elsevier, vol. 264(PB).
    4. Lv, Rongjian & Li, Hua & Sun, Qiubai & Gao, Qiyue & Li, Bowen, 2026. "Evolution of group behaviour in the ecological snowdrift game-level-headed and impatient delayed epidemic model under emergencies," Applied Mathematics and Computation, Elsevier, vol. 509(C).

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