Non-pharmaceutical interventions and the emergence of pathogen variants

Abstract

Non-pharmaceutical interventions (NPIs), such as social distancing and contact tracing, are important public health measures that can reduce pathogen transmission. In addition to playing a crucial role in suppressing transmission, NPIs influence pathogen evolution by mediating mutation supply, restricting the availability of susceptible hosts, and altering the strength of selection for novel variants. Yet it is unclear how NPIs might affect the emergence of novel variants that are able to escape pre-existing immunity (partially or fully), are more transmissible or cause greater mortality. We analyse a stochastic two-strain epidemiological model to determine how the strength and timing of NPIs affect the emergence of variants with similar or contrasting life-history characteristics to the wild type. We show that, while stronger and timelier NPIs generally reduce the likelihood of variant emergence, it is possible for more transmissible variants with high cross-immunity to have a greater probability of emerging at intermediate levels of NPIs. This is because intermediate levels of NPIs allow an epidemic of the wild type that is neither too small (facilitating high mutation supply), nor too large (leaving a large pool of susceptible hosts), to prevent a novel variant from becoming established in the host population. However, since one cannot predict the characteristics of a variant, the best strategy to prevent emergence is likely to be an implementation of strong, timely NPIs.

Keywords: cross-immunity; immune escape; lockdowns; pathogen evolution; social distancing; transmissibility.

Figure 1.

Model schematic. Arrows show transitions between classes at the given rates, with parameters as described in the main text

Figure 2.

Effects of the strength of NPIs $(r)$, strength of cross-immunity $(c)$ and relative transmissibility of the variant $({\beta }_v/{\beta }_w$; as indicated at the top of each column on (a–d) median proportion of hosts infected by the variant; (e–h) median total deaths (per 100k) for both strains; and (i–l) the probability of the variant emerging (reaching a frequency of at least 0.1). Each measure is calculated over the full duration of each simulation. NPIs are triggered at the start of each simulation and remain in place throughout. Other parameters as described in the main text, with $\frac{{\alpha }_w}{{\alpha }_w+\gamma }=\frac{1}{50}$ and ${\alpha }_v={\alpha }_w$

Figure 3.

Simulations with full cross-immunity and a 50% more transmissible variant $(\frac{{\beta }_v}{{\beta }_w}=1.5)$ for different levels of NPIs (triggered at the start of the simulation and in place throughout): (a, d) no NPIs $(r=0)$; (b, e) intermediate NPIs $(r=0.5)$; (c, f) strong NPIs $(r=0.75)$. (a–c) Proportion of the entire population currently infected by the wild type (blue) and by the variant (red), with coinfected contributing to both counts. (d–f) Frequency of the variant. Simulations were terminated when the pathogen went extinct. Other parameters as described in the main text, with $\frac{{\alpha }_w}{{\alpha }_w+\gamma }=\frac{1}{50}$ and ${\alpha }_v={\alpha }_w$

Figure 4.

Effects of NPIs $(r)$ and the relative virulence $({\alpha }_v/{\alpha }_w)$ of a twice as transmissible variant $({\beta }_v/{\beta }_w=2)$ on total deaths (per 100k) when there is full cross-immunity $(c=1)$ and NPIs are introduced at the start of the simulation and remain in place throughout. Plots show the median number of deaths (black) along with the upper and lower quartiles (grey). Other parameters as described in the main text with $\frac{{\alpha }_w}{{\alpha }_w+\gamma }=\frac{1}{50}$

Figure 5.

Effects of the strength of NPIs $(r)$ when there are NPI trigger thresholds, strength of cross-immunity $(c)$ and relative transmissibility of the variant $({\beta }_v/{\beta }_w$; as indicated at the top of each column on (a–d) median proportion of hosts infected by the variant; (e–h) median total deaths (per 100k) for both strains; and (i–l) the probability of the variant emerging (reaching a frequency of at least 0.1). The NPI trigger thresholds are ${ϵ}_{\mathrm{o}\mathrm{n}}=0.01$ and ${ϵ}_{\mathrm{o}\mathrm{f}\mathrm{f}}=0.002$ (i.e. NPIs are triggered when 1% of the host population is infected by either strain, and are removed when only 0.2% are infected). Other parameters as described in the main text, with $\frac{{\alpha }_w}{{\alpha }_w+\gamma }=\frac{1}{50}$ and ${\alpha }_v={\alpha }_w$

Figure 6.

Effects of NPIs $(r)$ and the relative virulence $({\alpha }_v/{\alpha }_w)$ of a variant that is twice as transmissible $({\beta }_v/{\beta }_w=2)$ on total deaths (per 100k) when there is full cross-immunity $(c=1)$ and NPIs have trigger and relaxation thresholds $({ϵ}_{\mathrm{o}\mathrm{n}}=0.01$ and ${ϵ}_{\mathrm{o}\mathrm{f}\mathrm{f}}=0.002)$. Plots show the median number of deaths (black) along with the upper and lower quartiles (grey). Other parameters as described in the main text with $\frac{{\alpha }_w}{{\alpha }_w+\gamma }=\frac{1}{50}$