Mathematical modeling is a useful tool in the study of virus dynamics for many types of viruses such as HCV, HBV, HPV, HIV, and Covid-19. It can be used to predict behavior under certain conditions or decide which parameters enhance the spread of disease. It may also be used to calculate the medications required to eradicate the disease or, at least, get it under control. These models can be used also to understand the biological mechanisms and interpret the experimental results. In general, numerical solutions were obtained for the models. However, analytical solutions could be useful for the estimation of parameters and for direct and simple predictions for the viral loads. Seldom, an analytical or an approximate analytical solution can be found in the literature. In this research work, an approximate analytical solution is obtained for the standard model. Similar standard models have been used for HCV, HBV, HIV, and Covid-19 in the literature. Nevertheless, the model considered is the HCV model. There is no reduction for the system of ODE or assumptions to simplify the equations of the model. Yet, the approximation is in the solution not in the system of differential equations. Therefore, it is more accurate and satisfactory than the previously mentioned analytical solutions.

## Why is it important?

The mathematical model for the standard model for hepatitis C virus (HCV) is considered in detail; however, the analysis and results can be applicable for all other viruses including Covid-19. This standard model is used to study viral dynamics in patients treated with direct-acting antiviral agents. The case of no treatment can be directly obtained. Given that medical specialists and physicians are more interested in solutions that yield direct and simple predictions, it is expected that the proposed approximate analytical solution would be attractive to them and help them to obtain a straightforward and a proper estimation regarding the viral load due to variations in treatment and/or patient’s parameters.