Our estimate of R for MERS-CoV was 0.73 (0.54—0.96), whereas in a single-type branching process model R = 0.63 (0.49—0.85).

Using a multi-type branching process , we developed an inference framework to make better use of age-structured outbreak size data.

In a single-type branching process framework, the threshold is a single number: the total size of the outbreak [31, 16].

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.

We compared these values with estimates from an inference framework based on a single-type branching process [15, 16, 17, 18].

This bias is the result of our assumption that introductions occur randomly across the susceptible population, and illustrates an important caveat to inference of R from the mean outbreak size in a single-type branching process model.

However, existing techniques for estimating transmission potential from outbreak size data generally represent transmission in the host population using single-type branching process [15, 16, 17, 18].

We made use of this observation by developing a novel age-structured model of stuttering transmission chains, which combined reported social contact data with a multi-type branching process [23, 24].

We used a multi-type branching process to model secondary infections (see Text 81 for details).

Estimates of R0 and relative susceptibility, S, when simulation model is a multi-type branching process with 15 age groups.

Text, it follows that the 8* cell dynamics reduce to a subcritical branching process,

Mathematically, these dynamics are summarized as a two-type branching process , see also Fig.

Since the 8 cells in (1) undergo a critical branching process , their progeny will eventually go extinct (see also the discussion of 8*< cells below).

From this it is easy to see that the dynamics of the 8* cell population in the basal layer are governed by the continuous-time critical branching process

The subcritical branching process model above was derived under the assumption of a well-mixed basal layer where infected cells are surrounded primarily by susceptible cells.

Immune capacity in the branching process model.

First, time to clearance is generally longer in the branching process model: the three dotted horizontal lines correspond to the three quartiles for the (M/fi_ = 1)distribution in Fig.

Only for the (,u/fi_ = 8) -distri-bution, which corresponds to an 8-fold increase in immune capacity, are all three quartiles of the spatial model below the corresponding quartiles of the branching process model.

This is due to the fact that, in contrast to the branching process model, elimination of an infected cell can trigger division of an 8* cell (with probability 195* > 0), therefore compensating for the loss of the infected cell and delaying clearance.

To study the joint effect of drug heterogeneity, growth rate, and evolution of resistance, we analyze a multi-type stochastic branching process describing growth of cancer cells in multiple compartments with different drug concentrations and limited migration between compartments.

The backward equations for this branching process are (see 81 Text for how to derive them)

Nevertheless, using the multiplicative properties of branching processes , we can calculate the probability of escape and the (conditional) average time to resistance for any given initial conditions of tumor size or metastases (see derivation details in 81 Text).

In this way, the two competing pathways can be seen as three-type branching processes , respectively, with different fitness

Since we are considering a branching process , larger population size is more likely to generate resistant mutation.