Investigation of the stochastic behaviour of a COVID-19 transmission model

In this study, the stochastic behavior of the spread of COVID-19 disease is examined by using a deterministic differential equation system available in the literature. Using the analysis of the stochastic system obtained by adding stochastic noise to the model published by Ahmed et al., the randomness in the spread of the disease is discussed. The source model differs from other COVID-19 transmission models in the literature with its six-compartment structure, in which quarantined and exposed individuals, as well as symptomatic and asymptomatic individuals are represented. With the stochastic analysis of this model, it is aimed to examine the progression of the disease in the population in a different way. The obtained stochastic differential equation system is numerically analyzed by both Euler-Maruyama and Milstein methods, which are widely used in literature. By means of numerical solutions obtained for the compartments, the average stochastic solutions are found, and these solutions are compared with the solutions of the deterministic model, and the random structure related to the disease is analyzed. For the deterministic model, the stochastic structure of disease spread is discussed by examining different indicators such as the information from the basic reproduction number given in the source study, average stochastic numerical solutions, extreme values obtained by different stochastic methods, and solution graphs. In addition, the solutions obtained from changing the method used in stochastic simulation, the number of repetitions and the values of the diffusion coefficients are discussed. During the examination of the obtained stochastic model, a detailed analysis of the stochastic system is aimed through the comparison of the changes in these components with each other and with the deterministic solution.