Numerical solution of mathematical models of some infectious diseases with meshless methods

In this thesis, numerical solutions of mathematical models of tuberculosis and influenza infectious diseases were calculated using the collocation method with radial basis functions. Fractional diffusion effective and ineffective SIR mathematical model for tuberculosis disease, fractional diffusion effective and ineffective SEIR mathematical model for influenza disease are discussed. Caputo derivative was chosen as the fraction derivative operator. Numerical results of the diffusion-ineffective SIR mathematical model were obtained using Euler and fourth-order Runge-Kutta (RK4). In the method discussed, Gaussian and Multiquadric basis functions were used in collocation method with radial basis functions used in solving diffusion-effective mathematical models. Numerical solutions were obtained for four different orders of fraction derivatives in both models. SIR and SEIR mathematical models have been investigated with and without diffusion effect. In diffusion effect models, calculations of both derivative orders and diffusion effects were made separately for three different positions. The numerical values obtained for tuberculosis in Turkey are given in tables and graphs in comparison with the number of patients in the 2021 Report of Tuberculosis War in Turkey. All numerical results obtained were compared in terms of basis functions, derivative orders, diffusion coefficients and positions.