COMPUTATIONAL MODELING OF COEXISTENCE OF VIRUS STRAINS: UNPREDICTABILITY BECAUSE OF NONLINEAR PHENOMENA
DOI:
https://doi.org/10.11603/mie.1996-1960.2020.1.11128Keywords:
epidemiology, endemic state, stability, deterministic chaos, nonlinear analysisAbstract
Background. The model of interaction of two strains of the virus is considered in the paper. The model is based on a system of differential equations and takes into account populations of susceptible, first-time and re-infected individuals across two strains. The objective of the work was to offer and investigate the model of coexistence of two virus strain from viewpoint of stability, periodicity and predictability of the epidemiological curves.
Materials and methods. Results. As a mathematical object a system of seven ordinary differential equations was proposed. At the same time, more sophisticated models based on delayed differential equations, stochastic differential equations, partial differential derivative equations can be used in the study of the spatial spread of the epidemic. Of great importance in all these cases is a qualitative study of the nonlinear behavior of the model. We see from numerical studies that at certain values of the parameters of the solution, large values of periods are obtained. Such solutions are called quasi-periodic and correspond to a situation called in the theory of dynamical systems as "deterministic chaos".
The obtained solution trajectories of the proposed model also indicate the complexity of epidemic prediction. Even in the simplest case of describing a model based on deterministic equations, we get chaotic solutions. This is due to the complexity of nonlinear interaction between subpopulations of the epidemiological model.
Conclusions. The model of coexistence of two strains of viruses was investigated. Such a model can be used to investigate the spread of infectious diseases. Of great importance in the model are the subpopulations of individuals susceptible to the virus, given its two strains. It is undoubted that further studies should address the use of a seasonal spread of epidemiological^ relevant disease that is consistent with the use of non-stationary dynamic models. Also of great importance is the inclusion in the model of populations of symptomatically and asymptotically infected persons.
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