When the infection was introduced into the under 20 age group , there was an asymmetry in the threshold for an unusually large outbreak in the UK (Fig.

As the infection was introduced in the youngest group, this suggested that chains of transmission were more likely to persist if they crossed into the eldest age group .

This implies that having a single case in the introductory age group and several in the other group was unlikely when R0 = 0.7.

Such immunity will not necessary be distributed evenly across the population: if pathogens circulate over an extended period of time, or vaccination campaigns have been discontinued, preexisting immunity is more likely to be found in older age groups [12].

Preexisting immunity in older age groups can alter this pattern [22] , making it possible to separate the reproduction number into its pathogen and popu-lation-specific components.

First we derived an expression for the outbreak size distribution in an age-stratified population, in which transmission between different age groups depended on the number of physical contacts reported in the POLYMOD survey in Great Britain.

We explored the age pattern of infection by calculating the joint outbreak size distribution across different age groups .

When the infection was introduced into the under 20 age group , the outbreak size distribution was therefore relatively symmetric between the two groups (Fig.

If infection started in the under 20 age group , there was a noticeable bias in the outbreak size distribution, with large outbreaks in under 20 year-olds more likely than large outbreaks in the over 20s

While the relative risks for DM1 patients are highest in the age group 65—70 with values from 1.9—2.3 for these diseases, we find higher risks for DM2 patients at younger ages, e.g.

We test 1 051 possible comorbidities for 19 age groups for DM1 and DMZ, giving 39 938 tests.

This leads to a multiple hypothesis testing problem for each age group where 1 051 hypotheses are tested in parallel.

The sex ratio SR(x,t) is related to the quotient of the percentage of female and male diabetes patients in age group tthat also have diagnoses x or are prescribed a medication x. Denote the number of male (female) DM1 and DM2 patients in age group tby Dmog(t) and the number of male (female) diabetes patients Who also have diagnoses or medication x by me(x,t).

Each diagnosis where the null hypothesis of statistical independence with either DM1 or DMZ can be rejected with a given value of the false discovery rate in at least one of the age groups is identified as a comorbidity.

The comorbidities are also listed in the supplement, SI Table, along with relative risks, p-values, and patient ages for the age group with the smallest p-values for DM1 and DMZ, respectively.

For the age groups with the smallest p-value the relative risks RR, patient ages, and the corresponding p-values are shown for DM1 and DM2, respectively.

Comorbidity data for DMl patients, the relative risks RRI, the confidence intervals for RRI, if applicable the p-Value for the co-occurrence analysis, and the sex ratio for each diagnosis and age group .

Comorbidity data for DM2 patients, the relative risks RRZ, the confidence intervals for RRZ, if applicable the p-Value for the co-occurrence analysis, and the sex ratio for each diagnosis and age group .

There has also been a shift over the same time period in the age group reporting the largest number of cases (aside from infants), from adolescents to 7—11 year olds.

There has also been a shift over the same time period in the age group reporting the largest number of cases (aside from infants), from adolescents to 7—11 year olds.

These differences caused a shift in the age distribution of pertussis disease incidence: the adolescent peak in years prior to 2006 shifted to a younger age group (5—10 year olds) post-2006.

The mixing matrix fi(i, j) represents the product of the contact rate (obtained from the ‘POLYMOD’ diary study of contact patterns in Great Britain (GB) [43]) and the transmission probability per contact between individuals in age groups 1' and j.

Pertussis case count data from NNDSS were aggregated into annual counts for each age group so that yl- (t) is the number of pertussis disease cases for age group i in year t. Our mathematical model outputs were also aggregated into annual counts for each age group i, so that x,- (t) was the model-derived case count for age group 1', during year t. These model-derived case counts are functions of the model structure and parameters, so that they might be better expressed as x,- (t|0, M), where 0 represents the parameter vector for model M.

Only data in under 5 year old children were considered because carriage information in older age groups is sparse and indirect effects, both VT elimination and serotype replacement, in those age groups , take longer to reach maximum impact.

The validity of our results should hold for other pneumococcal disease endpoints, including non-bacteraemic pneumonia, other age groups , in particular the elderly, and conjugate vaccine formulations of higher valency; data to validate this expectation are only recently becoming available.

However, still only limited information on nasopharyngeal carriage in older age groups , particularly in elderly is collected [24] and in many settings no carriage information is available.