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SIR model with non-local force of infection

Author

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  • Silva Rodrigues, Bárbara
  • Rebelo, Magda
  • Patrício, Paula

Abstract

Spatial dependence is incorporated into an SIR model with a non-local force of infection by accounting for continuously distributed contacts across space. This leads to a system of integro-differential equations. For this spatial model, the existence and uniqueness of solutions have been established, and the basic reproduction number, R0, has been defined via the next-generation operator. The relationship between the stability of the disease-free equilibrium and the basic reproduction number has been established. A numerical method is proposed to approximate the basic reproduction number. Numerical simulations explore different scenarios of spatial heterogeneity in comparison with the homogeneous case. The epidemiological implications of these scenarios are analysed, including sensitivity to the initial location of the outbreak, as well as the influence of population density and contact distribution on disease dynamics and endemic equilibria.

Suggested Citation

  • Silva Rodrigues, Bárbara & Rebelo, Magda & Patrício, Paula, 2026. "SIR model with non-local force of infection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 249(C), pages 229-249.
    • Handle: RePEc:eee:matcom:v:249:y:2026:i:c:p:229-249
    DOI: 10.1016/j.matcom.2026.05.009
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