Stochastic approach to a delayed in-host model of DENV transmission

Abstract Motivation. The immune response to the viral transmission experiences delays due to diverse biological factors and is affected by several factors. These include infection rate, rate of apoptosis and impact of the antibody-virus complex which exhibit unpredictable nature in a random environment. Objective. The main goal is to examine the impact of noise terms, introduced into every state variable, on a delayed in-host model of viral transmission. Methodology. To determine the intensity fluctuations and variances of all concerned state variables in the stochastic delayed model, which includes a constant delay and Gaussian white noise, the Fourier transformation method is employed. Results and Conclusions. The limiting value of the delay parameter is derived explicitly as well as numerically. The system experiences Hopf bifurcation, whenever the delay parameter crosses the limiting value which is shown graphically. The intensities and variances of different cells and virus populations are derived and the values are computed numerically. As the delay increases, the level of viremia decreases while other parameters maintain fixed values. The outcomes of data sensitivity, shown in graphical form, indicate that the transmission rate and supply rate of viruses are highly sensitive. Our findings suggest that the presence of noise causes fluctuations in the delayed model, leading to a noticeable impact on the transmission of the virus.