Modeling the dynamics of epidemics of infectious diseases under conditions of diffusion perturbations

Fìz.-mat. model. ìnf. tehnol. 2021, 32:58-63

Abstract

The paper proposes a modification of the SIRS epidemic model to take into account the influence of diffusion perturbations on the dynamics of the spread of an infectious disease. A singularly perturbed model problem with delay is reduced to a sequence of problems without delay. The sought functions are represented in asymptotic series as perturbations of solutions of the corresponding degenerate problems. The results of numerical experiments illustrating the influence of spatially distributed diffusion redistributions on the spread of an infectious disease are presented.

References

1. Kermack, W. O., McKendrick, A. G. (1991). Contributions to the mathematical theory of epidemics – I. Bulletin of Mathematical Biology, 53(1-2), 33–55.
   DOI doi.org/10.1016/s0092-8240(05)80040-0
2. Brauer, F., Castillo-Chavez, C., Feng, Z. 2019. Mathematical Models in Epidemiology. New York: Springer.
3. Källén, A., Arcuri, P., Murray, J.,D. (1985). A simple model for the spatial spread and control of rabies. J. Theor. Biol., 116, 377–393.
   DOI doi.org/10.1016/s0022-5193(85)80276-9
4. Sun, G.-Q. (2012). Pattern formation of an epidemic model with diffusion. Nonlinear Dynamics, 69(3), 1097–1104.
5. Bomba, A. Ya, Baranovsky, S. V., Pasichnyk, M. S., Pryshchepa, O. V. (2020). Modeling small-scale spatial distributed influences on the development of infectious disease process. Mathematical modeling and computing, 7(2), 310–321.
   DOI doi.org/10.1109/csit49958.2020.9322047
6. Bomba А., Baranovskii, S. Pasichnyk, M., Malash, O. V. K. (2020). Modeling of Infectious Disease Dynamics under the Conditions of Spatial Perturbations and Taking into account Impulse Effects. Proceedings of the 3rd International Conference on Informatics & Data-Driven Medicine (IDDM 2020), Växjö, Sweden. –
7. Elsgolt, L. E., Norkin, S. B. (1971). Vvedeniye v teoriyu differentsial'nykh uravneniy s otklonyayushchimsya argumentom.– M.: Nauka.
8. Bomba, A. Ya., Baranovskyy, S. V., Prysyazhnyuk, I. M. (2008). Neliniyni synhulyarno zbureni zadachi typu «konvektsiya-dyfuziya». – Rivne: NUVHP.
9. Klyushin, D. A., Lyashko, S. I., Lyashko, N. I., Bondar, O. S., Tymoshenko, A. A. (2020). Generalized optimization of processes of drug transport in tumors. Cybernetics and System Analisys, 56(5), 758-765.
   DOI doi.org/10.1007/s10559-020-00296-9
10. Sandrakov, G. V., Lyashko, S. I., Bondar, E. S., Lyashko, N. I. (2019). Modeling and optimization of microneedle systems. Journal of Automation and Information Sciences, 51(6), 1-11.
    DOI doi.org/10.1615/jautomatinfscien.v51.i6.10