A theoretical analysis of stochastic epidemiological models under delay and fractional brownian motion
This study examined selected nonlinear Stochastic Differential Equations arising in disease modeling. The main objective of this study was to include randomness into the dynamics of tuberculosis and HIV. Stochasticity to the models was introduced through perturbation of parameters which is a standard method in stochastic population modeling. The well-posedness analysis of SDEs included the existence of non-negative solutions as required in the dynamics of population modeling. A detailed stability analysis of results, analytical properties and asymptotical behavior of solutions was also done. The mean reverting process was approximated for one of the variables in the TB and HIV models and the mean and variance of the process was found.