Virus propagation with randomness

Viruses are organisms that need to infect a host cell in order to reproduce. The new viruses leave the infected cell and look for other susceptible cells to infect. The mathematical models for virus propagation are very similar to population and epidemic models, and involve a relatively large number of parameters. These parameters are very difficult to establish with accuracy, while variability in the cell and virus populations and measurement errors are also to be expected. To deal with this issue, we consider the parameters to be random variables with given distributions. We use a non-intrusive variant of the polynomial chaos method to obtain statistics from the differential equations of two different virus models. The equations to be solved remain the same as in the deterministic case; thus no new computer codes need to be developed. Some examples are presented.