A mathematical model for the role of vaccination and treatment in measles transmission in Turkey

Abstract

A previously developed and analyzed deterministic model for the transmission dynamics of measles, which takes into account the possibility of vaccinated people also contracting the disease, has been developed for Turkey. The model consists of nine compartments. The structural identifiability of the model was examined using software and detailed tables are given assuming that the incidence is given for structural identifiability. As a result of this analysis, the model is found to be structurally identifiable if at least two parameters are given along with the incidence. The parameters in this non-autonomous model are determined by considering the 1970–2021 measles case numbers in Turkey. We realize that the changes in immigration rates in Turkey, especially since the early 2000s, the changes in vaccination rates from 1970 to the present, and the changes in the vaccination rates of susceptible individuals, are significant changes in terms of time, and so we assume that these three parameters are time dependent. The practical identifiability of the model with the determined parameters is examined and it is found that if two parameters are given, all parameters except five parameters are practical identifiable. Unidentified parameters are fixed to a value by taking reference sources into account, and a model with all parameters practically identifiable is achieved. With the obtained values, the associated reproduction number of the model was obtained as 1.07 which means that the disease will persist in Turkey.