Stochastic perspective to a SIVA in-host model of DENV transmission

Abstract The viral transmission is a complex process which is influenced by certain factors such as infection rate, production rate of new viruses and impact of the antibody-virus complex. These factors affect the transmission process unpredictably under the influence of external noise. In order to incorporate this phenomenon, the viral transmission is manifested under random environment by introducing noise to the deterministic SIVA model which is formulated by dividing the dynamical system into four distinct parts, namely, susceptible cells ( S ), infected cells ( I ), virus ( V ) and immune cells ( A ). A deterministic viral transmission model is analyzed as a representation of real-life situations that involves certain assumptions. In order to derive the intensity fluctuations and variances of the cell and virus population of the stochastic model with the presence of Gaussian white noise, Fourier transformation method is used. The deterministic model exhibits two distinct equilibria: virus-free steady (VFS) and endemic steady (ES) state. The intensities and variances of different cells and virus populations are derived and the values are computed numerically. The results of the sensitivity analysis, shown in graphical form, indicate that the infection rate and the production rate of viruses are highly sensitive. Our findings suggest that the presence of noise causes fluctuations in the model, leading to a noticeable impact on the transmission of the virus.