# 1.3.1. The mathematics of virus replication and transmission

Viruses are obligatory cell parasites and as such are capable of rapid, exponential growth. This is particularly the case for viral replication within individual organisms. This means that the virus replication dynamics can range from linear (when the virus persists as a covert infection, with minimal replication) all the way to fully logarithmic (when the virus is growing exponentially) and back to linear again when the maximum virus load within diseased or dying organisms is reached, due to exhaustion of the resources for replication (Fig. 2).

The epidemiological spread between organisms is influenced by the transmission medium (air, water, vector), whose rules of dispersion are often not fully exponential. This also applies to other barriers to virus proliferation, such as tissue-specificity, interference, auto-interference, RNA silencing, and immune reactions which all can influence virus multiplication, shedding and dispersal. These restrictions can temper the logarithmic character of the quantitative virus data distribution, at the individual bee, colony or regional level.

What this means is that, from the design of
experiments through to the analysis of the data, allowance has to be made for
non-linear distributions of the data, ranging from fully logarithmic
(pathogenic replication) through semi-exponential (epidemic proliferation) to
near-linear (covert replication, dispersal). This can be addressed through
transformations, thresholds or non-linear models, but it MUST be dealt with
appropriately. Guidelines for this can be found in detail in the *BEEBOOK* paper on statistical methods
(Pirk *et al.,* 2013), with aspects
specific to virus research also covered in section 3; “Statistical Aspects” of
this chapter.