We simulated outbreaks using a multi-type branching process with two groups, then used the outbreak size distribution to infer R0 and relative immunity in older individuals.

First, we examined two infections with the same R0 = 0.2, but different levels of immunity in the over 20 age group.

We simulated 50 spillover events, and found the maximum likelihood estimate of R0 and S. We repeated this process for 1000 sets of outbreaks, obtaining reliable estimates of both R0 and 8 (Figs.

We used the outbreak size distribution to identify what constitutes an anomalously large outbreak for a particular R0 .

If R0 = 0.7, a chain of at least 8 cases was not unusual if some of the secondary cases are children, yet it is if the secondary cases are all adults.

2A, when R0 = 0.7 an outbreak of size 7 was anomalously large if all secondary cases were in the youngest group, but an outbreak of size 10 was not unusual if between 2—8 secondary cases were in the eldest group.

We assumed a fully susceptible population, which meant that the average number of secondary cases generated by a typical infectious individual was equal to the basic reproduction number, R0 [9].

Using nested models, it was shown that in order to maXimise the epidemiological (between-host) reproductive ratio R0 , increasing the growth rate might not always be the best option for a pathogen because it shortens the duration of the infection.

Principally, [27] aimed to determine the longterm R0 across a population, while our model concerns the emergence of new strains intra-host.

In addition, [27] used deterministic equations, and did not investigate the stochastic emergence of new strains (that is, whether those with a smaller R0 are likely to emerge if they appear at a low frequency).

To give an example, when applied to a model of pathogen emergence in an SIR setting, the effective reproductive ratio Rl< would equal the standard reproductive ratio R0 , reduced by a factor So/N, if there initially existed So susceptible individuals out of a total population of size N. There would also be a term in the denominator that is proportional to the rate of spread of the initial, unmutated strain.

We use the notation R1 to draw parallels between the scaled pathogenic replication rate, and the reproductive ratio R0 in population-level, epidemiological models [32].

where r0 is the baseline firing rate, 0 g m g 1 is the modulation index, and f0 is the oscillation frequency.

The magnitude of the peak power and its relation to the baseline power are dependent on multiple factors; namely r0 , T, m. Thus, a measure that is independent of subjective properties is required Which we term the modulation index (161).

However, when there is no underlying oscillation in that frequency, the result will tend to be zero, as the value of SPT(f;£ f0) approaches r0 , as shown in Eq 5.

how r0 varies as a function of time since the target jump).

where r0 = 0.

We used the value function at t = 0 to determine the optimal initial reach angle x0* for each possible initial belief r0 , i.e.