Modeling the Virus Infection at the Population Level

Abstract

As pointed out by many researchers in the last few decades, differential equations with fractional (non-integer) order differential operators, in comparison with classical integer order ones, have apparent advantages in modeling. A Caputo fractional order system of ordinary differential equations is introduced to model the virus infection at the population level in this chapter. As well known, there are two main methods to study the dynamics of a model: qualitative analysis and numerical modeling. Here the qualitative analysis, including uniqueness, invariant set, and stability, is first presented with intuitive derivation. Then the famous genetic algorithm is introduced to numerically model the dynamics of virus infection, i.e. to adjust the parameters of the Caputo fractional model such that its solution can properly fit real data and predict future.

Keywords: Caputo fractional model; Numerical modeling; Qualitative analysis; Virus infection at the population level.