Mathematical modeling of infectious diseases

Mathematical models are widely used in social sciences, life sciences, economics and politics, especially in epidemiology. These models can be used to estimate basic parameters, such as the total number of future cases and deaths, and to analyse the impact of measures taken to control the epidemic. Both deterministic and stochastic models have been used in the literature to understand infectious diseases and make future predictions. In this thesis, various models such as SIRD, SIRS, SEIR, SEIRS, MSEIR and MSEIRS are derived from the deterministic SIR model by adding different compartments to it. In addition, since deterministic models do not fully reflect the real-life variability, a stochastic SIR model obtained by adding Brownian motion (Wiener process) to the equations in the deterministic SIR model is considered. In the application section, COVID-19 patient numbers for Turkey are evaluated using official data. The transmission coefficient is calculated using the maximum likelihood parameter estimation method, and the recovery coefficient is determined by considering the 14-day COVID-19 recovery period. The deterministic equation is solved numerically using the Euler method, while stochastic equation is solved numerically using the Euler-Maruyama method. Graphical analyses of susceptible, infected and recovered individuals are obtained using MATLAB.