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20

Viruses

20.1

Virus Structure and Life Cycle

A complete virus (virion) is essentially a piece of packaged genetic material (the

provirus). The protein packaging (called envelope or capsid) around the DNA or

RNA protects its integrity; this packaging is in turn usually encapsulated in a protein

coat, which is able to bind to specific target hosts.

A virus first attaches to its host, penetrates inside the cell, and removes its coat to

release its genetic material (RNA or DNA). The encoded genes are expressed (using

the machinery of the host) and replicated. Copies of the viruses are then assembled

from the expressed genes, and released, usually by lysis of the host cell, which

kills it, and the cycle begins again. ⁴ Hence, this is called the lytic pathway. Some

viruses can alternately select the lysogenic or dormant pathway, whereby the virus is

incorporated into the host’s genome. In this case it is only replicated when the host

cell divides. The switching mechanism between the lytic and lysogenic pathways

provides a good example of a regulatory network. ⁵

Mathematical modelling has been especially valuable for gaining insight into

how a viral infection spreads within a host because many details are not directly

experimentally accessible. ⁶

20.2

Viruses as Pathogens

Many viruses are pathogenic to human beings, some extremely so. An effective way

of modelling the spread of viral diseases (and indeed any infectious disease) is the

susceptible–infected–recovered model illustrated in Fig. 20.1. It is described by three

differential equations:

ds

dt ^{= −βsi}

(20.1)

di

dt ^{= βsi − ρi}

(20.2)

dr

dt ^{= ρi}

(20.3)

where ss is the fraction of susceptible people in a total population upper NN, ii the fraction

of infected people, and rr the fraction of recovered people, with

s plus i plus r equals 1 periods + i + r = 1 .

(20.4)

4 See, e.g., Ryu (2017) for elaboration of many details.

5 Vohradsky (2001), Vohradsky (2017), Shao et al. (2019).

6 Graw and Perelson (2016).