Mathematical modeling of some seasonal dynamics in the spread of infectious diseases

In this thesis, compartmental epidemiological models such as SIR, SEIR and SVEIR are considered in accordance with the transmission dynamics of measles and mathematical analyses of the selected models are performed. The basic reproduction rate, if any, is calculated for the epidemics to occur under the effect of demographic changes, immigration and vaccination processes, and this value is associated with the stability of the equilibria of the system. Then, in order to examine the cases where the disease does not disappear completely and shows seasonal exacerbations, the rate of transmission is chosen as a time-dependent function in the demographic structured SIR model. It has been shown that the basic reproduction number should be handled differently from the constant parameter case, and the peak moment t of the epidemic is calculated. The results of the study are supported by numerical simulations related to the created scenarios, for the transmission dynamics of measles