Yuqumli kasalliklar rivojlanish dinamikasini matematik modellashtirish
Mathematical modeling of infectious disease dynamics
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The article analyzes the compartmental SEIR model describing the dynamics of infectious disease spread in a population. It presents the formulation of the model as a system of ordinary differential equations, the threshold role of the basic reproduction number R0, the stability of the disease-free equilibrium and the equation determining the final epidemic size. A numerical experiment for a hypothetical population of 100,000 showed that as R0 increases from 1.4 to 4.9, the epidemic peak shifts from day 247 to day 51, while the final attack rate rises from 51.1% to 99.2%. It is shown that at R0 = 3.5 no epidemic occurs when 75% of the population has pre-existing immunity.
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