for a wide range of directly transmitted infectious diseases , the household plays a pivotal 
         role in transmission due to the greater strength of contacts between individuals sharing 
         living arrangements [ 1 , 2 ] .
we can conceptualize many infections as transmitting readily to 
         household members , but transmitting at a lower rate to individuals in the wider community . 
        
this concept led to both early work on quantifying these effects using clinical data   and to more recent attempts to incorporate 
         households into models of pandemic influenza in britain [ 46 ] .
a large body of 
         modelling work explores the spread of infection in populations structured into households , 
         considering both thresholds for large - scale epidemics and optimal deployment of vaccination 
         ( see [ 79 ] and references therein ) .
however , this work has largely been 
         theoretical and has often not sought to relate results to available data or to consider 
         vaccination measures that would be practically achievable . here
we consider household models 
         relevant to the spread of pandemic influenza , and using data from the 2001 census examine 
         the range of geographical heterogeneities in early epidemic behaviour .
recent concerns over pandemic influenza have prompted a cascade of model development [ 4 , 1017 ] with many models 
         acknowledging the role played by households and structure the population and transmission 
         accordingly [ 4 , 10 ] .
some of these models are highly complex , and consider the role of 
         transmission in households , schools and workplaces as well as incorporating localized 
         spatial transmission [ 10 , 12 ] . here
we take a simpler approach and focus exclusively on the 
         implications of strong household transmission together with weaker transmission to the local 
         community .
our model ( see online supplementary information , and ) and analysis operate at the scale of wards ; there are around 10 
         000 wards in great britain ( england , wales and scotland ) with populations of between 1000 
         and 35 000 individuals in each according to the 2001 census .
the aggregation scale used in 
         this paper is the 2001 census standard table wards  referred to simply as wards 
         throughout  although strictly speaking such standard table wards are distinct 
         from ( but related to ) both other statistical wards , and also electoral wards used in local 
         government .
the mathematical model essentially provides a sophisticated and dedicated tool 
         for translating demographic characteristics into epidemiological properties .
we begin by considering household sizes and number of dependent children , both in terms of 
         distributions within great britain and in terms of variability between wards . using our 
         household model ,
this variability is translated into early expected growth rates of an 
         epidemic allowing us to explore the geographical distribution of this most important 
         epidemiological quantity .
finally , we consider the advantages of prophylactic vaccination 
         targeted towards dependent children compared to vaccination at random or focused towards 
         entire households .
households consisting of just one or two individuals 
         dominate , with decreasing numbers of households with larger occupancy ( fig . 1 
 a ) .
we note that the 2001 census does not contain precise information on 
         households containing eight or more occupants , and therefore assume in our model that values 
         of  eight or more are exactly eight , which makes little quantitative or 
         qualitative difference to our results compared to any other realistic approach .
this 
         variability in household size is clearly important : large households have a greater chance 
         of being infected ( as there are more members to potentially bring infection in from the 
         community ) and a higher rate of internal transmission ( due to the greater number of 
         contacts ) .
however , quantifying the impact of these features requires the type of detailed 
         mathematical model developed in the next section ( and online supplementary information ) . 

( a ) the distribution of household sizes plotted as 
               the total number of households of each size in great britain .
( b ) the 
               proportions of households with a given number of dependent children separated into 
               household sizes .
( c ) the distribution of dependent children as 
               percentages of the ward population size .
( d ) the correlation between 
               percentage of dependent children and the mean household size within a ward ; dots 
               represent the values for each of the 9976 standard table wards in great britain ; a 
               simple linear fit and associated confidence intervals are shown in red .
crown copyright material is reproduced with the permission of the 
               controller of hmso . ) 
 
( a ) the distribution of household sizes plotted as 
               the total number of households of each size in great britain .
( b ) the 
               proportions of households with a given number of dependent children separated into 
               household sizes .
( c ) the distribution of dependent children as 
               percentages of the ward population size .
( d ) the correlation between 
               percentage of dependent children and the mean household size within a ward ; dots 
               represent the values for each of the 9976 standard table wards in great britain ; a 
               simple linear fit and associated confidence intervals are shown in red .
crown copyright material is reproduced with the permission of the 
               controller of hmso . )
given the importance of large households it is important to consider their composition in 
         more detail and to determine relationships with other demographic measures . considering 
         dependent children ( fig . 1 
 b ) we find , as expected , that larger households tend to have more dependent 
         children . as such less than 10% of households of five or more
are solely occupied by adults , 
         whereas over 90% of households of size two have no dependent children . for this
we can see 
         that numbers of dependent children and household sizes are closely linked .
we observe , as 
         shown in figure 1 
 c , great geographic diversity in the proportion of dependent children in 
         each ward  while the average is around 23% , extremes as low as 5% and as high as 
         40% exist . finally , we observe that the proportion of dependent children within a ward 
         closely correlates with the average household size in that ward ( fig .
1d ) , although we note that there are several 
         points this figure exhibiting large mean household size but with few dependent children ; the 
         demographic features ( such as student houseshares ) that can lead to this are discussed more 
         fully in the supplementary information .
it is against the above background of heterogeneous host demography that our mathematical 
         model operates .
our model of household - based transmission is relatively simple and parsimonious , and aims 
           to identify the effects of different household patterns across great britain .
two 
           transmission rates are used : transmission between members of the same household and 
           transmission to general members of the local population ( ward ) .
transmission between wards 
           is not included , for model simplicity and transparency of results . while movement between 
           wards and continuous importation of infection from abroad are likely to have a significant 
           impact on the behaviour of pandemic influenza , these operate at a different scale from 
           household - level transmission and so as a first approximation can be ignored .
the general 
           spread of infection within the ward community is modelled as frequency - dependent 
           transmission , in accordance with general modelling of large human populations [ 19 , 20 ] , 
           while transmission within the household is assumed to be density dependent , such that 
           individuals interact in a pairwise manner irrespective of household size . in practice
, 
           household transmission probably lies between the extremes of frequency and density 
           dependence , but the precise scaling is 
           likely depend on the type of household and ages of occupants . by assuming such 
           density - dependent transmission we are maximizing the degree of heterogeneity  
           other assumptions produce weaker results but do not effect the qualitative conclusions .
although our modelling framework can deal with a range of dynamic aspects of infection , 
           here we simply consider the early ( asymptotic ) growth rate of infection within each ward . 
          
in particular , a range of standard theory shows that starting with a low level of 
           infection within the population , and following some initial short - lived transients , the 
           disease incidence and prevalence is predicted to increase exponentially [ 20 , 22 , 
             23 ] ; it is this early exponential growth rate 
           that is of primary interest here .
in particular , we seek the  basic reproductive 
           ratio , r0 , defined such that the early growth of 
           infected cases ( i ) is given by 
             i(t)~exp([r01]gt ) 
           where 1/g is the average infectious period .
we note that this value of 
             r0 defined in terms of growth rates differs from the 
             r0 defined in terms of number of secondary cases ; although 
           both agree at the invasion threshold 
             r0=r0=1 ( see online 
           supplementary information for a more detailed discussion ) .
we decided to use 
             r0 as its definition most closely matches observations taken 
           during an epidemic . while a relatively simple formulation , our model is parameterized to match observables 
           concerning pandemic influenza . using the national distribution of household sizes , we fix 
           the household and community transmission rates to yield a 40% chance of transmission 
           between any two household members ( often called the secondary attack 
           rate ) and
a basic reproductive ratio of approximately 2 for great britain as a 
           whole , which is consistent with statistical work in this field [ 1 , 2 ] .
figure 2 shows the geographical distribution of 
           basic reproductive ratios ( r0 values ) in each ward in great 
           britain .
we observe in figure 2 
 b an approximate 25% variation in r0 between 
           the mean and most extreme wards , which corresponds to a 50% variation in early epidemic 
           growth rates . in general , high growth rates reflect a greater than average abundance of 
           large household sizes and high proportion of dependent children , although the precise 
           relationship is complex and nonlinear .
it is clear from both the locations of wards with 
           highest r0 ( fig .
2 
 a ) , and the discussion in the supplementary information , that high values 
           of r0 tend to be associated with the large conurbations of 
           great britain , with the areas of highest r0 having around 20 
           times the mean population density of great britain .
epidemiologically , those wards with 
           the highest r0 will require the greatest levels of control and 
           therefore may be targeted with high priority during an epidemic ; in addition , the fact 
           that these high r0 wards are generally in urban areas may mean 
           that pandemic influenza ( or any other novel pathogen ) is likely to enter such wards early 
           in a national epidemic . 
 fig .
2distribution of r0 values in great britain , 
                 highlighting the predicted variation in early epidemic growth rates . 
                
( a ) wards are shown in their geographic locations and coloured 
                 according to their r0 value .
the histograms in 
                   ( b ) utilize the same colour scale and hence provide a reference 
                 for the ward - based map .
( electronic information on ward boundaries is census output , 
                 which is crown copyright and is reproduced with the permission of the controller of 
                 hmso and the queen 's printer for scotland .
crown copyright 2003 . ) 
  distribution of r0 values in great britain , 
                 highlighting the predicted variation in early epidemic growth rates . 
                
( a ) wards are shown in their geographic locations and coloured 
                 according to their r0 value .
the histograms in 
                   ( b ) utilize the same colour scale and hence provide a reference 
                 for the ward - based map .
( electronic information on ward boundaries is census output , 
                 which is crown copyright and is reproduced with the permission of the controller of 
                 hmso and the queen 's printer for scotland .
prophylactic vaccination may be a key epidemiological tool in combating any future uk 
           epidemic , either to eliminate completely the risk of a large - scale epidemic or to be used 
           in conjunction with other methods such a social distancing , antivirals or contact tracing 
             . for simplicity ,
this efficacy does not change our qualitative 
           results but will make any vaccination strategy less effective .
figure 3 
 a considers three methods of targeting the delivery of vaccination within 
           wards , with the results for each ward displayed as a point .
the results of our household 
           model agree with previous findings in terms of the critical level of vaccination coverage 
           required to prevent an outbreak . 
          
this 
           is because effective herd immunity at the household level can be achieved without the need 
           to vaccinate all household members ; in essence vaccine is being wasted on individuals who 
           already have some protection through being in partially vaccinated households .
vaccinating 
           individuals at random ( red ) is a simpler and better strategy , and is found to outperform 
           the expected vaccination threshold ( black line ) predicted by simpler unstructured models 
             [ 19 , 20 , 26 ] .
the improvement over the 
           prediction from unstructured models is because random vaccination of individuals 
           effectively biases vaccination towards larger households , thereby targeting control at 
           these most epidemiologically important units .
however , an ideally targeted strategy    prioritizing individuals in 
           households with the most susceptibles  has even greater benefits with the 
           required level of critical vaccination never exceeding the random - mixing prediction of 
           50% .
we see overall that ideal targeting can reduce by about 40% the amount of vaccine 
           required nationally . 

( a ) critical levels of vaccine coverage 
                 needed to prevent the spread of infection within a ward are shown for three 
                 strategies , along with the prediction from standard models in which there is no 
                 population structure .
( b ) the effects on the distribution of ward 
                   rv values of three vaccination strategies .
these 
                 distributions are calculated at individual level since ward - level results are 
                 slightly biased by the trend for less populated wards to have smaller household 
                 sizes .
the box - whisker plots show the mean , 1 and 2 standard deviations and 
                 outliers .
( d ) comparison of the ward - level effects of vaccinating 
                 dependent children and heterogeneous random vaccination , in which the same 
                 proportion of each ward is vaccinated .
the nine exceptional wards in which 
                 heterogeneous random vaccination outperforms vaccinating dependent children are 
                 highlighted ( red circles ) in plots ( c ) and 
               ( d ) . 
 
( a ) critical levels of vaccine coverage 
                 needed to prevent the spread of infection within a ward are shown for three 
                 strategies , along with the prediction from standard models in which there is no 
                 population structure .
( b ) the effects on the distribution of ward 
                   rv values of three vaccination strategies .
these 
                 distributions are calculated at individual level since ward - level results are 
                 slightly biased by the trend for less populated wards to have smaller household 
                 sizes .
the box - whisker plots show the mean , 1 and 2 standard deviations and 
                 outliers .
( d ) comparison of the ward - level effects of vaccinating 
                 dependent children and heterogeneous random vaccination , in which the same 
                 proportion of each ward is vaccinated .
the nine exceptional wards in which 
                 heterogeneous random vaccination outperforms vaccinating dependent children are 
                 highlighted ( red circles ) in plots ( c ) and 
               ( d ) .
therefore we seek an alternative proxy that incorporates insights from the 
           ideal strategy and readily allows vaccination to be targeted towards a proportion of 
           individuals in the larger households . from figure 1 
 b
we predict that vaccinating children biases protection towards the 
           larger households , yet does not waste vaccine immunizing all members ; in addition it is 
           likely to be both ethically and socially acceptable . with this in mind ,
we consider three 
           forms of vaccination at the ward level : ( 1 ) vaccination of dependent children ( who account 
           for about 23% of the gb population ) ; ( 2 ) heterogeneous random vaccination , where 
           individuals are vaccinated at random with the proportion vaccinated equal to the 
           proportion of children within the ward ; and ( 3 ) homogeneous random vaccination , where 
           individuals are vaccinated at random in every ward , such that the proportion vaccinated 
           nationally matches the proportion of dependent children . alternatively
, we can consider 
           heterogeneous and homogeneous vaccination as randomizations of the vaccination of 
           dependent children ; heterogeneous vaccination randomizes the distribution of vaccine 
           within each ward , whereas homogeneous vaccination randomizes the distribution of vaccine 
           over the whole of great britain .
as such , comparing these three strategies allow us to 
           access the impact of targeting children , both in terms of efficient deployment within a 
           ward and also as a means of proportioning vaccine between wards .
even though all three 
           strategies ultimately vaccinate the same number of individuals ( around 23% of the 
           population ) , it is clear that targeting has advantages ( fig .
we measure the efficacy of vaccination through 
             rv ( the equivalent of r0 , but 
           after vaccination ) . vaccinating dependent children
causes a 35% drop in this reproductive 
           ratio ( from 2 to 13 ) , whereas both homogeneous and 
           heterogeneous vaccination only cause a reduction of around 25% .
comparing homogeneous and heterogeneous vaccination in more detail allows us to assess 
           the impact of targeting wards with the most children , without targeting large families 
           within those wards .
the histograms and box - whisker plots of rv 
           show that the targeting inherent in heterogeneous vaccination offers negligible mean 
           benefit over homogeneous vaccination ( fig .
however , this ward - level targeting does significantly reduce the 
           variability in epidemic growth rates bringing those wards with extremely high growth rates 
           under greater control .
figure 3 ( c , 
           d ) considers the behaviour at the ward level , with particular focus on 
             r0 before vaccination and the equivalent measure 
             rv after a proportion of the population has been vaccinated . 
           in general targeting vaccination towards dependent children not only
reduces the average 
           reproductive ratio ( rv ) but also significantly reduces much of 
           the variability ( fig .
wards that originally had high r0 values 
           due to large average household sizes with many children are now brought much closer to the 
           average . in only nine wards ( red circles ) out of over 10
meaning that at a local as well as a national scale vaccinating children is overwhelmingly 
           effective .
the precise socio - demographic characteristics of these nine outliers is 
           explored more fully in the supplementary material , but all these wards have either large 
           student or older adult households , breaking the general rule that large households are 
           associated with many dependent children .
our model of household - based transmission is relatively simple and parsimonious , and aims 
           to identify the effects of different household patterns across great britain .
two 
           transmission rates are used : transmission between members of the same household and 
           transmission to general members of the local population ( ward ) .
transmission between wards 
           is not included , for model simplicity and transparency of results . while movement between 
           wards and continuous importation of infection from abroad are likely to have a significant 
           impact on the behaviour of pandemic influenza , these operate at a different scale from 
           household - level transmission and so as a first approximation can be ignored .
the general 
           spread of infection within the ward community is modelled as frequency - dependent 
           transmission , in accordance with general modelling of large human populations [ 19 , 20 ] , 
           while transmission within the household is assumed to be density dependent , such that 
           individuals interact in a pairwise manner irrespective of household size . in practice
, 
           household transmission probably lies between the extremes of frequency and density 
           dependence , but the precise scaling is 
           likely depend on the type of household and ages of occupants . by assuming such 
           density - dependent transmission we are maximizing the degree of heterogeneity  
          
although our modelling framework can deal with a range of dynamic aspects of infection , 
           here we simply consider the early ( asymptotic ) growth rate of infection within each ward . 
          
in particular , a range of standard theory shows that starting with a low level of 
           infection within the population , and following some initial short - lived transients , the 
           disease incidence and prevalence is predicted to increase exponentially [ 20 , 22 , 
             23 ] ; it is this early exponential growth rate 
           that is of primary interest here . in particular , we seek the  basic reproductive 
           ratio , r0 , defined such that the early growth of 
           infected cases ( i ) is given by 
             i(t)~exp([r01]gt ) 
           where 1/g is the average infectious period .
we note that this value of 
             r0 defined in terms of growth rates differs from the 
             r0 defined in terms of number of secondary cases ; although 
           both agree at the invasion threshold 
             r0=r0=1 ( see online 
           supplementary information for a more detailed discussion ) .
we decided to use 
             r0 as its definition most closely matches observations taken 
           during an epidemic . while a relatively simple formulation , our model is parameterized to match observables 
           concerning pandemic influenza . using the national distribution of household sizes , we fix 
           the household and community transmission rates to yield a 40% chance of transmission 
           between any two household members ( often called the secondary attack 
           rate ) and a basic reproductive ratio of approximately 2 for great britain as a 
           whole , which is consistent with statistical work in this field [ 1 , 2 ] . our qualitative 
           conclusions are robust to the precise choice of parameters . figure 2 shows the geographical distribution of 
           basic reproductive ratios ( r0 values ) in each ward in great 
           britain .
we observe in figure 2 
 b an approximate 25% variation in r0 between 
           the mean and most extreme wards , which corresponds to a 50% variation in early epidemic 
           growth rates . in general , high growth rates reflect a greater than average abundance of 
           large household sizes and high proportion of dependent children , although the precise 
           relationship is complex and nonlinear .
it is clear from both the locations of wards with 
           highest r0 ( fig . 2 
 a ) , and the discussion in the supplementary information , that high values 
           of r0 tend to be associated with the large conurbations of 
           great britain , with the areas of highest r0 having around 20 
           times the mean population density of great britain .
epidemiologically , those wards with 
           the highest r0 will require the greatest levels of control and 
           therefore may be targeted with high priority during an epidemic ; in addition , the fact 
           that these high r0 wards are generally in urban areas may mean 
           that pandemic influenza ( or any other novel pathogen ) is likely to enter such wards early 
           in a national epidemic . 
 fig .
2distribution of r0 values in great britain , 
                 highlighting the predicted variation in early epidemic growth rates . 
                
( a ) wards are shown in their geographic locations and coloured 
                 according to their r0 value .
the histograms in 
                   ( b ) utilize the same colour scale and hence provide a reference 
                 for the ward - based map .
( electronic information on ward boundaries is census output , 
                 which is crown copyright and is reproduced with the permission of the controller of 
                 hmso and the queen 's printer for scotland . source : 2001 census , output area 
                 boundaries [ 28 , 29 ] .
crown copyright 2003 . ) 
  distribution of r0 values in great britain , 
                 highlighting the predicted variation in early epidemic growth rates . 
                
( a ) wards are shown in their geographic locations and coloured 
                 according to their r0 value .
the histograms in 
                   ( b ) utilize the same colour scale and hence provide a reference 
                 for the ward - based map .
( electronic information on ward boundaries is census output , 
                 which is crown copyright and is reproduced with the permission of the controller of 
                 hmso and the queen 's printer for scotland .
prophylactic vaccination may be a key epidemiological tool in combating any future uk 
           epidemic , either to eliminate completely the risk of a large - scale epidemic or to be used 
           in conjunction with other methods such a social distancing , antivirals or contact tracing 
             . for simplicity ,
this efficacy does not change our qualitative 
           results but will make any vaccination strategy less effective .
figure 3 
 a considers three methods of targeting the delivery of vaccination within 
           wards , with the results for each ward displayed as a point .
the results of our household 
           model agree with previous findings in terms of the critical level of vaccination coverage 
           required to prevent an outbreak . 
          
this 
           is because effective herd immunity at the household level can be achieved without the need 
           to vaccinate all household members ; in essence vaccine is being wasted on individuals who 
           already have some protection through being in partially vaccinated households . vaccinating 
           individuals at random ( red )
is a simpler and better strategy , and is found to outperform 
           the expected vaccination threshold ( black line ) predicted by simpler unstructured models 
             [ 19 , 20 , 26 ] .
the improvement over the 
           prediction from unstructured models is because random vaccination of individuals 
           effectively biases vaccination towards larger households , thereby targeting control at 
           these most epidemiologically important units .
however , an ideally targeted strategy    prioritizing individuals in 
           households with the most susceptibles  has even greater benefits with the 
           required level of critical vaccination never exceeding the random - mixing prediction of 
           50% .
we see overall that ideal targeting can reduce by about 40% the amount of vaccine 
           required nationally . 

( a ) critical levels of vaccine coverage 
                 needed to prevent the spread of infection within a ward are shown for three 
                 strategies , along with the prediction from standard models in which there is no 
                 population structure .
( b ) the effects on the distribution of ward 
                   rv values of three vaccination strategies .
these 
                 distributions are calculated at individual level since ward - level results are 
                 slightly biased by the trend for less populated wards to have smaller household 
                 sizes .
the box - whisker plots show the mean , 1 and 2 standard deviations and 
                 outliers .
( d ) comparison of the ward - level effects of vaccinating 
                 dependent children and heterogeneous random vaccination , in which the same 
                 proportion of each ward is vaccinated .
the nine exceptional wards in which 
                 heterogeneous random vaccination outperforms vaccinating dependent children are 
                 highlighted ( red circles ) in plots ( c ) and 
               ( d ) . 
 
( a ) critical levels of vaccine coverage 
                 needed to prevent the spread of infection within a ward are shown for three 
                 strategies , along with the prediction from standard models in which there is no 
                 population structure .
( b ) the effects on the distribution of ward 
                   rv values of three vaccination strategies .
these 
                 distributions are calculated at individual level since ward - level results are 
                 slightly biased by the trend for less populated wards to have smaller household 
                 sizes .
the box - whisker plots show the mean , 1 and 2 standard deviations and 
                 outliers .
( d ) comparison of the ward - level effects of vaccinating 
                 dependent children and heterogeneous random vaccination , in which the same 
                 proportion of each ward is vaccinated .
the nine exceptional wards in which 
                 heterogeneous random vaccination outperforms vaccinating dependent children are 
                 highlighted ( red circles ) in plots ( c ) and 
               ( d ) .
therefore we seek an alternative proxy that incorporates insights from the 
           ideal strategy and readily allows vaccination to be targeted towards a proportion of 
           individuals in the larger households . from figure 1 
 b
we predict that vaccinating children biases protection towards the 
           larger households , yet does not waste vaccine immunizing all members ; in addition it is 
           likely to be both ethically and socially acceptable . with this in mind ,
we consider three 
           forms of vaccination at the ward level : ( 1 ) vaccination of dependent children ( who account 
           for about 23% of the gb population ) ; ( 2 ) heterogeneous random vaccination , where 
           individuals are vaccinated at random with the proportion vaccinated equal to the 
           proportion of children within the ward ; and ( 3 ) homogeneous random vaccination , where 
           individuals are vaccinated at random in every ward , such that the proportion vaccinated 
           nationally matches the proportion of dependent children . alternatively
, we can consider 
           heterogeneous and homogeneous vaccination as randomizations of the vaccination of 
           dependent children ; heterogeneous vaccination randomizes the distribution of vaccine 
           within each ward , whereas homogeneous vaccination randomizes the distribution of vaccine 
           over the whole of great britain . as such , comparing these three strategies allow us to 
           access the impact of targeting children , both in terms of efficient deployment within a 
           ward and also as a means of proportioning vaccine between wards .
even though all three 
           strategies ultimately vaccinate the same number of individuals ( around 23% of the 
           population ) , it is clear that targeting has advantages ( fig .
we measure the efficacy of vaccination through 
             rv ( the equivalent of r0 , but 
           after vaccination ) .
vaccinating dependent children causes a 35% drop in this reproductive 
           ratio ( from 2 to 13 ) , whereas both homogeneous and 
           heterogeneous vaccination only cause a reduction of around 25% .
comparing homogeneous and heterogeneous vaccination in more detail allows us to assess 
           the impact of targeting wards with the most children , without targeting large families 
           within those wards .
the histograms and box - whisker plots of rv 
           show that the targeting inherent in heterogeneous vaccination offers negligible mean 
           benefit over homogeneous vaccination ( fig .
however , this ward - level targeting does significantly reduce the 
           variability in epidemic growth rates bringing those wards with extremely high growth rates 
           under greater control .
figure 3 ( c , 
           d ) considers the behaviour at the ward level , with particular focus on 
             r0 before vaccination and the equivalent measure 
             rv after a proportion of the population has been vaccinated . 
           in general targeting vaccination towards dependent children
not only reduces the average 
           reproductive ratio ( rv ) but also significantly reduces much of 
           the variability ( fig .
wards that originally had high r0 values 
           due to large average household sizes with many children are now brought much closer to the 
           average . in only nine wards ( red circles ) out of over 10
meaning that at a local as well as a national scale vaccinating children is overwhelmingly 
           effective .
the precise socio - demographic characteristics of these nine outliers is 
           explored more fully in the supplementary material , but all these wards have either large 
           student or older adult households , breaking the general rule that large households are 
           associated with many dependent children .
there are a wide range of regional heterogeneities within great britain which it may be 
         very important to capture or appreciate if detailed mathematical models are to be 
         effectively used in containment planning .
our results follow the general epidemiological 
         tenet that such heterogeneities can be used to target control measures efficiently .
however , 
         ideal targeting is impractical and socially unacceptable ; instead we show that targeting 
         prophylactic vaccination towards dependent children may be an effective ( and acceptable ) 
         means of targeting intervention towards the largest and therefore most epidemiologically 
         important households , without the disadvantages associated with vaccinating entire 
         households .
we have also found an interesting demographic pattern in the small number 
         ( < 01% ) of wards that do not obey this rule , which are dominated either by 
         student or older adult socio - demographic categories .
our model is obviously a simplification of the complex reality of pandemic ' flu 
         transmission in great britain ; however , our model is sufficiently detailed to highlight the 
         role that household structure can play and the implications of geographic heterogeneities 
         recorded in the 2001 census .
the simplifying assumptions that we believe to be most relevant 
         when considering extensions to our work are as follows .
first , we assume a compartmental 
         paradigm where individuals are either susceptible , infectious or recovered . in reality , 
         pathogen levels and infectiousness vary during the course of infection and also between 
         individuals .
second , we have assumed that the strength of contacts between individuals 
         within a household and between members of the general population are independent of 
         household size .
finally , we have ignored other geographic diversities in assuming that the 
         general rate of transmission in the population is the same across great britain , when in 
         fact it is likely to be higher in areas with higher population density , bigger workplaces 
         and busier transport links , which will probably inflate the variation already observed . bearing these limitations in mind , we believe that modelling offers a good tool for 
         understanding socio - demographic patterns and their epidemiological consequences . in 
         particular , our work on household structure offers the robust conclusion that vaccination of 
         children is expected to be an effective approach to control of emergent infectious diseases , 
         since it targets vaccine towards both wards and households with the greatest transmission 
         risk .
furthermore , vaccinating children is likely to be socially acceptable and although not 
         sufficient to prevent an epidemic may help to support other control measures such as social 
         distancing , antimicrobial drugs or quarantine .
finally , we believe that insights from our 
         work can be useful in evaluation and planning of schemes for control of diseases with 
         existing childhood vaccination schemes ( such as measles ) where the geographic diversity in 
         epidemiologically relevant quantities that we have considered here may prove important for 
         prioritization of efforts to maintain and increase uptake of vaccine . in this context
it is 
         interesting to note that the numbers of gp surgeries and statistical wards in the uk is 
         approximately equal , leading to equivalent levels of geographic diversity .
 summaryone of the central tenets of modern infectious disease epidemiology is that an 
           understanding of heterogeneities , both in host demography and transmission , allows control 
           to be efficiently optimized . due to the strong interactions present , households are one of 
           the most important heterogeneities to consider , both in terms of predicting epidemic 
           severity and as a target for intervention . 
 we consider these effects in the context of 
           pandemic influenza in great britain , and find that there is significant local ( ward - level ) 
           variation in the basic reproductive ratio , with some regions predicted to suffer 50% 
           faster growth rate of infection than the mean . 
 childhood vaccination was shown to be 
           highly effective at controlling an epidemic , generally outperforming random vaccination 
           and substantially reducing the variation between regions ; only nine out of over 10 000 
           wards did not obey this rule and these can be identified as demographically atypical 
           regions . since these benefits of childhood vaccination are a product of correlations 
           between household size and number of dependent children in the household , our results are 
           qualitatively robust for a variety of disease scenarios . 
INTRODUCTION
DEMOGRAPHIC PATTERNS IN GREAT BRITAIN
Geographic distribution of early growth rates
Control by vaccination
DISCUSSION