Modified finite difference method using random sampling for nonlinear epidemic models / Maha Abduljabbar Mohammed - Maha Abduljabbar , Mohammed (2018)
In this thesis, new modified numerical simulation processes are proposed to solve social epidemic models in the form of nonlinear initial value problems (IVP) of ordinary differential equations with multiple random variable parameters. The variables of the systems are dependent on time . The utilization of Monte Carlo (MC) simulation with central divided difference formula is repeated times to simulate values of the variable parameters of the Spain weight reduction model as random sampling instead being limited as real values with respect to time. The mean of the final solutions via this integrated technique, named in short as Mean Monte Carlo Finite Difference (MMCFD) method, represents the final solution of the system. The numerical outputs are tabulated, graphed and compared with previous statistical estimations for 2013, 2015 and 2030 respectively. The solutions of FD and MMCFD are found to be in good agreement with small standard deviation of mean and small measure of difference. In the social epidemic of cocaine abuse in Spain, the FD numerical method is integrated with Latin hypercube sampling (LHS) technique in every simulation to simulate random variable parameters for the stochasticdeterministic model. The mean of final solutions of the FD iterations is known as Mean Latin Hypercube Finite Difference (MLHFD) solutions. The results obtained are compared with deterministic solutions of classical FD and homotopy analysis methods as relative to the previous statistical estimations from 1995 to 2015. Good agreement between the two is perceived with small errors. The MLHFD results are tabulated, graphed and discussed pertaining to the model's expected behavior until 2045. MMCFD and MLHFD are proposed for the first time in this thesis to calculate and to predict future behavior of the epidemic models considered. The results show the range for random distribution for the present numerical solutions obtained are in good agreement and approximation as compared to the existing randomized statistical estimations.