Analytical solution for post-death transmission model of Ebola epidemics

摘要

In this paper, we shall introduce deceased human (D) transmission to the cycle phenomenon of disease modelling, which has a direct relationship with the infective compartment of the stochastic Susceptible-Infected-Recovered (SIR) disease model. Due to this, the noise covariance matrices of the standard stochastic SIR model will be modified. This will be done by using van Kampen's expansion method to approximate the master equation and the stochastic Fokker–Planck equation to analytically calculate a power spectral density (PSD) expression. A vector-valued process is used and shows that the absolute value of the real part of the principal diagonal of the PSD matrix solution is the spectral density of the system which is compared to the average PSD of the stochastic simulations. We aim to investigate the problem of identifiability when deceased humans act as an extended state of host infection using the SIR-D model during Ebola epidemics. Using our analytical solution model, we show that for an increasing degree of transmission parameter values the infected route cannot be identified, whereas the deceased human transmission shows enhancement for the persistence of Ebola virus disease using epidemiology data of the Democratic Republic of Congo.