Incorporating Time Delays in the Mathematical Modelling of the Human Immune Response in Viral Infections

Mathematical modelling helps to describe the functional and causal relationships between objects in the physical world. The complexity of these models increases as more components and variables are added to maintain and observe. Differential equations are regularly used in these models, as they are able to display the interactions between several variables and describe non-linear behaviour. Differential equations are commonly used in immune response mathematical models to help describe these complex and dynamic interactions within the immune system of the organism. Time delays in the immune system are common and are often disregarded due to the low-resolution of models, which provide limited description of the specific section of immune system being studied. The few models that incorporate time delays are mostly at the epidemiological level, to track the spread of the virus in the population. In this paper we review the applications of the models based on differential equations and describe their potential utilization for the studies of immune response in SARS-CoV-2.