The use of Mathematical Models of Epidemics for Analysis of influence of Preventive Measures on the Epidemic Situation Indices

Student: Arepev Stepan

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Applied Mathematics (Bachelor)

Final Grade: 9

Year of Graduation: 2016

An epidemic model based on the model with loss of immunity is considered. Epidemic process is divided into 3 stages depending on outer factors. At the first stage it is common SIRS process. The second and the third stages correspond to an increase of disease and further decline in morbidity. In this case additional parameters are introduced. We study both stochastic and deterministic realizations of the model. For the stochastic realization two-dimensional Markov chain is constructed, Kolmogorov equations for the transition probabilities are written. We formulate the optimal control problem to find the best time to start the vaccination and solve it numerically.

Full text (added May 28, 2016)

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