Analysis of an epidemic mathematical model based on delay differential equations

We propose a mathematical model of infection spreading among the adult population of certain region. The model is constructed on the basis of some delay differential equations that are supplemented with integral equations of convolution type and the initial data. The variables included in the integral equations and the delay variables take into account the number of individuals in different groups and the transition rate of individuals between the groups which reflects the stages of the disease. Some properties of the solutions of the model are under study including the existence, uniqueness, and nonnegativity of the solution components on the half-axis, as well as the presence and stability of the equilibrium states. We formulate and solve the problem of eliminating infection during finite time. The time for infection eradication is estimated on using the exponentially decreasing component-by-component estimates of the solution. Also we present the results of computational experiments on estimating the eradication time and evaluating the effectiveness of the process of diagnosis and identification of sick (infected) individuals through the procedure of regular medical examinations.