Comparison on Virus Dynamics Models with Different Functional Responses Including Time Delays

Abstract

A virus can be identified as an infectious mediator consisting a core of genetic material and an envelope of protein. The behavior of viruses can be modelled through mathematics, and those viral dynamics can consist a class of differential equations which describe the effect of the virus on uninfected and infected cells, in a body compartment over a period of time. Even though many mathematical models have been proposed for various viral infections, a proper assessment on them has not been done throughout the literature. In this paper, dynamics models with bilinear, Michaelis Menten, saturated and Beddignton-DeAngelis functional responses have been compared, with respective to the time delays and the basic reproductive rate (0). For the considered models, the populations of uninfected cells, infected cells and free virus were calculated to find solutions for respective infection free and infected equilibriums. By carrying out numerical simulations through literature reported parameter values, the effect of intracellular and maturation time delays on the corresponding reproductive rate of each model was analyzed. Since a reproductive rate, less than unity represents an infection free host, the primary target of the treatments for viral infections is to decrease the reproductive rate as possible. The graphical representation showed that the model with BeddigntonDeAngelis functional response, possessed a greater capacity in reducing 0, with the effect of time delays. This qualitative analysis on models will have the capability to give the drug producers more significant guidance in recognizing the most appropriate viral dynamics model.