Mathematical modeling of measles outbreak with two patches

In this thesis, a model for measles, which is given in the form of SVEIS in the literature, is discussed. In 2001, the parameters in the single-patch mathematical SVEIS model were estimated by fitting data with the MATLAB program using data on measles in Turkey. A two-patch mathematical SVEIS model was created with the mutual migration or travel of both people who are susceptible to the disease and those who are sick from Turkey and the neighboring country. Disease-independent equilibrium points and basic proliferation numbers of the two models were found and stability theorems were given. Numerical results supporting the theory were obtained. Finally, the course of the measles epidemic was examined for four different situations, assuming that all other parameters except the measles transmission coefficient of the neighboring country, migration rate and initial values were the same as the parameter values in Turkey.