Table 1.

List of definitions of the model parameters and relevant equations, described in detail in the text.

Model Variables and Equations
number of hosts	N
maximum number of receptors per host	M
transmission time	$t_I$
cross-reactivity width	d
average mutation effect	$\sigma$
mutation rate	$\mu$
target fraction of infected hosts	${\overline{f}}_i$
probability of infection after exposure to the virus	$p_f$
cross-reactivity kernel	$f\left(r\right)=\exp (-\frac{r}{d})$
jump size distribution	$\rho (a\to b)=(1/2\pi )(4r_{ab}/{\sigma }^2)e^{-2r_{ab}/\sigma }$
probability of transmitting a mutated virus	$P_{\mathrm{mut}}=1-e^{-\mu t_I}$
average attempted transmissions per infection	$R_0=\frac{1}{\langle p_f\rangle }+\frac{{\overline{f}}_i-f_i}{{\overline{f}}_i}$