Viral Population Growth Models

The steps involved in viral reproduction are described briefly. Mathematical models for the growth of viral populations without random effects take the form of systems of differential equations and these are reviewed, including the standard HIV equations, with correction terms. The validity of the “mass action” assumption is questioned for low virion levels. Stochastic differential equation models for HIV are described, including those with both discontinuous and diffusion processes. Simulation results are given for early HIV population growth, including the distribution of the time to reach a detection level, for which an analytical theory is also available. The more complicated long-term model of Tan and Wu is discussed briefly as well as mutation and its effect on drug treatments. Although there has been some useful analysis of patient data with respect to simple differential equations, it is concluded that modeling, either deterministic or stochastic, of viral populations requires much further development to give an accurate and useful representation of the underlying biological processes.