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On solvability of one nonlinear integral equation arising in modelling of geographical spread of epidemics. (English) Zbl 1478.92199

Karapetyants, Alexey N. (ed.) et al., Operator theory and harmonic analysis. OTHA 2020, Part II – probability-analytical models, methods and applications. Based on the international conference on modern methods, problems and applications of operator theory and harmonic analysis. Cham: Springer. Springer Proc. Math. Stat. 358, 253-272 (2021).
Summary: In the present work, one nonlinear convolution integral equation on the whole line is considered. This equation arises in theory of temporal-spatial spread of epidemics. For the above equation, the existence and uniqueness theorems are proved. Based on theoretical convergence, results are applied to epidemic model with diffusion term, describing geographical spread of infection diseases. At the end of work for influenza epidemic, several numerical simulations are implemented.
For the entire collection see [Zbl 1470.46003].

MSC:

92D30 Epidemiology
45G05 Singular nonlinear integral equations
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