Modeling the influence of diffusion perturbations on the development of infectious diseases taking the convection and immunotherapy into account
Keywords:infectious disease model, dynamic systems, asymptotic methods, singularly perturbed problems
The mathematical model of the infectious disease is modified to account for the influence of diffusion perturbations and the convection on the dynamics of the immune response under immunotherapy. The solution of the corresponding singularly perturbed problem with time-delay is reduced to a sequence of solutions of problems without time-delay. Sought functions are represented in the form of asymptotic series as perturbations of solutions to the corresponding degenerate problems. We present the results of a numerical modeling that illustrate the influence of the diffusion redistribution of active factors on the infectious disease development under the immunotherapy conditions. The results demonstrate a decrease in the maximum concentration level of antigens in the locus of infection as a result of their diffusion redistribution.
Marchuk, G. L. (1997). Mathematical models of immune response in infectious diseases. Dordrecht: Kluwer Press.
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, No. 2, pp. 310-321. https://doi.org/10.23939/mmc2020.02.310
Bomba, А., Baranovskii, S., Pasichnyk, M. & Malash, K. (2020, November). Modeling of Infectious Disease Dynamics under the Conditions of Spatial Perturbations and Taking into account Impulse Effects. Proceedings of the 3rd International Conference Informatics & Data-Driven Medicine (IDDM 2020), (pp. 119-128), Växjö, Sweden.
Bomba, A. Ya. & Baranovsky, S. V. (2020). Modeling small-scale spatial distributed influences on the dynamics of infectious disease on condition of Pharmacotherapy. J. Numerical and Applied Mathematics. No. 1 (133), pp. 5-17. (in Ukrainian). https://doi.org/10.17721/2706-9699.2020.1.01
Klyushin, D. A., Lyashko, S. I., Lyashko, N. I., Bondar, O. S. & Tymoshenko, A. A. (2020). Generalized opti- mization of processes of drug transport in tumors. Cybernetics and System Analisys, 56, No. 5, pp. 758-765.
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, Iss. 6, pp.1-11. https://doi. org/10.1615/JAutomatInfScien. v51.i6.10.
Lyashko, S. I. & Semenov, V. V. (2001). On the controllability of linear distributed systems in classes of generalized actions. Cybernetics and Systems Analysis, 37, No.1, pp.13-32. https://doi.org/10.1023/ A:1016607831284
El'sgol'c, L. E. & Norkin, S. B. (1971). Introduction to the theory of differential equations with deviating argument. Moscow: Nauka. (in Russian).
Bomba, A. Ya., Baranovsky, S. V. & Prysyazhnyuk, I. M. (2008). Nonlinear singularly perturbed problems of the "convection-diffusion" type. Rivne: NUWEE. (in Ukrainian).
Bomba, A. Ya. (1982). Asymptotic method for approximately solving a mass transport problem for flow in a porous medium. Ukr. Math. Journal, 34, Iss. 4, pp. 400-403.
How to Cite
Copyright (c) 2021 Reports of the National Academy of Sciences of Ukraine
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.