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Uncertainty of initial conditions in a SEIR-model with vaccination

DOI 10.18127/j15604136-201906-07


V.V. Kotin – Ph.D. (Phys.-Math.), Associate Professor, Department “Medical and Technical Information Technology” (BMT-2), Bauman Moscow State Technical University
N.M. Chervyakov – Graduate Student, Department “Medical and Technical Information Technology” (BMT-2),
Bauman Moscow State Technical University

Mathematical models of the morbidity dynamics (often called “epidemiological models”) are traditionally considered extremely important for solving the problems of predicting and controlling human infectious diseases. The current urgency of this range of problems is due to such factors as large-scale migration of the population, the emergence of resistant pathogen strains and obviously growing need for an economic analysis of anti-epidemic procedures.
This paper analyzes the SEIR model of morbidity dynamics, taking into account migration and morbidity control effects (vaccination). Feasible sets and an integral funnel* for the SEIR system are found to evaluate extremely accessible control possibilities. The influence of the model input data (initial conditions) uncertainty is considered to determine the effectiveness of vaccination in the presence of initial conditions and migration flows uncertainty. The results obtained form the basis for choosing the most effective way to use limited resources during vaccination and other anti-epidemic measures such as isolation, quarantine and preventive treatment.

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