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Epidemiological dynamics of the 2009 Influenza A(H1N1)v outbreak in India

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We analyze the time-series data for the onset of A(H1N1)v influenza pandemic in India during the period June 1- September 30, 2009. Using a variety of statistical fitting procedures, we obtain a robust estimate of the exponential growth rate $\langle \lambda \rangle \simeq 0.15$. This corresponds to a basic reproductive number $R_0 \simeq 1.45$ for influenza A(H1N1)v in India, a value which lies towards the lower end of the range of values reported for different countries affected by the pandemic. Comment: 5 pages, 4 figures
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RESEARCH COMMUNICATIONS
CURRENT SCIENCE, VOL. 100, NO. 7, 10 APRIL 2011 1051
*For correspondence. (e-mail: sitabhra@imsc.res.in)
Epidemiological dynamics of the 2009
influenza A(H1N1)v outbreak in India
T. Jesan1,2, Gautam I. Menon1 and
Sitabhra Sinha1,*
1The Institute of Mathematical Sciences, CIT Campus, Taramani,
Chennai 600 113, India
2Health Physics Division, Bhabha Atomic Research Centre,
Kalpakkam 603 102, India
We analyse the time-series data for the onset of
A(H1N1)v influenza pandemic in India during the
period 1 June–30 September 2009. Using a variety of
statistical fitting procedures, we obtain a robust esti-
mate of the exponential growth rate
λ
j 0.15. This
corresponds to a basic reproduction number R0 j 1.45
for influenza A(H1N1)v in India, a value which lies
towards the lower end of the range of values reported
for different countries affected by the pandemic.
Keywords: Basic reproduction number, epidemic
dynamics, pandemic influenza, swine flu.
A NOVEL influenza strain termed influenza A(H1N1)v,
first identified in Mexico in March 2009, has rapidly
spread to different countries and is currently the pre-
dominant influenza virus in circulation worldwide1,2. As
of 11 April 2010, it has caused at least 17,798 deaths in
214 countries3. The first confirmed case in India, a pas-
senger arriving from USA, was detected on 16 May 2009
in Hyderabad. The initial cases were passengers arriving
by international flights. However, towards the end of
July, the infections appeared to have spread into the resi-
dent population with an increasing number of cases being
reported for people who had not been abroad. As of 11
April 2010, there have been 30,352 laboratory-confirmed
cases in India (out of 132,796 tested) and 1472 deaths
have been reported, i.e. 5% of the cases which tested
positive for influenza A(H1N1)v (ref. 4).
To devise effective strategies for combating the spread
of pandemic influenza A(H1N1), it is essential to esti-
mate the transmissibility of this disease in a reliable man-
ner. This is generally characterized by the reproductive
rate R, defined as the average number of secondary infec-
tions resulting from a single (primary) infection. A special
case is the basic reproduction number R0, which is the
value of R measured when the overall population is sus-
ceptible to the infection, as is the case at the initial stage
of an epidemic. Estimates of the basic reproduction num-
ber for influenza A(H1N1)v in reports published from
data obtained for different countries vary widely. For
example, R0 has been variously estimated to be between
2.2 and 3.0 for Mexico5, 1.72 for Mexico City6, between
1.4 and 1.6 for La Gloria in Mexico7, between 1.3 and 1.7
for the United States8 and 2.4 for the state of Victoria in
Australia9. The divergence in the estimates for the basic
reproduction number may be a result of under-reporting
in the early stages of the epidemic, or due to climatic
variations. They may also possibly reflect the effect of
different control strategies used in different regions, rang-
ing from social distancing such as school closures and
confinement to antiviral treatments.
In this communication, we estimate the basic reproduc-
tion number for the infections using the time-series of
infections in India extracted from reported data. By
assuming an exponential rise in the number of infected
cases I(t) during the initial stage of the epidemic when
most of the population is susceptible, we can express the
basic reproduction number as R0 = 1 +
λτ
(see e.g. Ander-
son and May10), where
λ
is the rate of exponential growth
in the number of infections and
τ
the mean generation in-
terval, which is approximately equal to 3 days6. Using the
time-series data, we obtain the slope
λ
of the exponential
growth using several different statistical techniques. Our
results show that this quantity has a value of around 0.15,
corresponding to R0 j 1.45.
We used data from the daily situation updates available
from the website of the Ministry of Health and Family
Welfare, Government of India (http://mohfw-h1n1.nic.in/).
In our analysis, data up to 30 September 2009 were used,
corresponding to a total of 10,078 positive cases. Note
that, after 30 September 2009, patients exhibiting mild
flu-like symptoms (classified as categories A and B) were
no longer tested for the presence of the influenza
A(H1N1) virus.
As the data exhibit very large fluctuations, with some
days not showing a single case while the following days
show extremely large number of cases, it is necessary to
smooth the data using a moving window average. We
have used an n-day moving average (n = 2–10), which
removes large fluctuations while remaining faithful to the
overall trend.
From the incidence data for the 2009 pandemic influ-
enza in India it appears that the disease has been largely
confined to the urban areas of the country. Indeed, six of
the seven largest metropolitan areas of India (which
together accommodate about 5% of the Indian population)
(http://www.world-gazetteer.com/; retrieved on 18 Febru-
ary 2010) account for 7139 infected cases up to 30 Sep-
tember 2009, i.e. 70.8% of the dataset we have used.
However, it is possible that this is a result of bias intro-
duced by the easier accessibility to testing facilities for
urban populations.
Figure 1 shows the daily number of confirmed infected
cases, as well as the 5-day moving average from 1 June to
30 September 2009, for the country as a whole and the
six major metropolitan areas which showed the highest
incidence of the disease: Hyderabad, Delhi, Bangalore,
Mumbai, Chennai and Pune. The adjoining map shows
the geographic locations of these six cities. In the period
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CURRENT SCIENCE, VOL. 100, NO. 7, 10 APRIL 2011
1052
Figure 1. Time-series of the number of infected cases (#Infected), of influenza A(H1N1)v showing the daily data (dot-
ted) as well as the 5-day moving average (solid line) for India and the six metropolitan areas with the highest number of
infections (whose geographic locations are shown in the adjoining map). The period shown is from 1 June to 30 Septem-
ber 2009. At the beginning of this period most of the infected people were arriving from abroad, while at the end of it the
infection was entrenched in the local population. The data reveal that almost all the cities showed a simultaneous increase
in the number of infections towards the end of July and the beginning of August. This is manifested as a sudden rise in
‘#Infected’ for India as a whole (note the semi-logarithmic scale), and can be taken as the period in which the infection
started spreading in the resident population.
Figure 2. a, Exponential slope
λ
estimated from the time-series data
of the number of infected cases (#Infected), averaged over a 5-day
period to smoothen the fluctuations (d, solid curve).
λ
is calculated by
considering the number of infected cases over a moving window having
different sizes (Δt), ranging between 7 and 36 days. By moving the
starting point of the window across the period 1 June–20 August (in
steps of 1 day) and calculating the best-fit linear slope of the data on a
semi-logarithmic scale (i.e. time in normal axis, number of infections in
logarithmic axis), we obtain an estimate of
λ
. The arrow indicates the
region between 28 July and 12 August (region within the broken lines),
which shows the largest increase in the number of infections within the
period under study, corresponding to the period when the epidemic
broke out in the resident population. Over this time-interval, the aver-
age of
λ
is calculated for the set of starting dates and window sizes
over which (b) the correlation coefficient r between log(#Infected) and
t, is greater than rcutoff (we consider 0.75 < rcutoff < 1 in our analysis),
and c, the measure of significance for the correlation p < 0.01.
up to July 2009, infections were largely reported in peo-
ple arriving from abroad. There is a marked increase in
the number of infections towards the end of July and the
beginning of August 2009 in all of these cities (note that
the ordinate is in logarithmic scale). This is manifest as a
sudden rise in the number of infected cases for the country
as a whole, implying that the infection started spreading
in the resident population in the approximate period of
28 July–August 12.
Figure 2 a shows the exponential slope
λ
estimated in
the following way. The time-series of the number of
infections is first smoothed by taking a 5-day moving
average. The resulting smoothed time-series is then used
to estimate
λ
by a regression procedure applied to the loga-
rithm of the number of infected cases [log(#infected)]
across a moving window of length Δt days. The origin of
the window is varied across the period 1 June–20 August
(in steps of 1 day). We then repeat the procedure by vary-
ing the length of the window over the range of 7–36 days.
To quantify the quality of regression, we calculate the
correlation coefficient r (Figure 2 b) between log (#In-
fected) and time (in days), and its measure of significance
p (Figure 2 c). The correlation coefficient r is bounded
between –1 and 1, with a value closer to 1 indicating a
good fit of the data to an exponential increase in the
number of infections. The measure of significance of the
fitting is expressed by the corresponding p value, which
expresses the probability of obtaining the same correla-
tion by random chance from uncorrelated data. The average
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CURRENT SCIENCE, VOL. 100, NO. 7, 10 APRIL 2011 1053
of the estimated exponential slope
λ
is obtained by taking
the mean of all values of
λ
obtained for windows origi-
nating between 28 July–12 August and of various sizes,
for which the correlation coefficient r > rcutoff (we con-
sider 0.75 < rcutoff < 1 in our analysis) and the measure of
significance p < 0.01. For comparison, we show again in
Figure 2 d the number of infected cases of H1N1 in India
(dotted) together with its 5-day moving average (solid
line). The horizontal broken lines running across the fig-
ure indicate the period between 28 July and 12 August,
which exhibited the highest increase in the number of
infections within the period under study (from 1 June to
30 September).
Figure 3 shows the average exponential slope
λ
as a
function of rcutoff, calculated for the original data and for
different periods n over which the moving average is
taken (n = 2, 3, 4, 5 and 10). For n = 3–5, the data show a
similar profile indicating the robustness of the estimate of
the average exponential slope
λ
with respect to different
values of n. The sudden increase in
λ
around rcutoff j 0.9
implies that beyond this region the slope depends sensi-
tively on the cut-off value. Considering the region where
the variation is smoother gives an approximate value
λ
~ 0.15, corresponding to a basic reproduction number
Figure 3. Average slope
λ
of the variation in log(#Infected) with
time t, as a function of the threshold of correlation coefficient, rcutoff,
used to filter the data. The averaging is performed for infections occur-
ring within the period 28 July–12 August (for details see caption to
Figure 2). Different symbols indicate the actual daily time-series data
(squares) and the data smoothed over a moving n-day period, with
n = 2 (right-pointed triangle), 3 (diamond), 4 (inverted triangle), 5 (cir-
cle) and 10 (triangle). The significance of the correlation between
log(#Infected) and time t, P < 0.01 for all data points used in perform-
ing the average. Note that for n = 3–5 the data show similar profiles for
variation of
λ
with rcutoff , indicating the robustness of the estimate
with respect to different values of n used. The sudden increase in the
value of the average slope around rcutoff j 0.9, implies that beyond this
region the slope depends sensitively on the cut-off value. Considering
the region where the variation is more gradual gives us an approximate
value of the slope
λ
~ 0.15, corresponding to a basic reproduction
number R0 j 1.45.
for the epidemic R0 = 1 +
λτ
j 1.45, assuming the mean
generation interval,
τ
= 3 days.
We compute the confidence bounds for the estimate of
R0 from the 5-day moving average time-series using the
‘confint’ function of the scientific software MATLAB
(http://www.mathworks.com/). This function generates the
goodness-of-fit statistics using the solution of the least
squares fitting of log(#Infected) to a linear function. It re-
sults in a mean value
λ
= 0.16, with the corresponding
95% confidence intervals calculated as [0.116, 0.206],
consistent with our previous estimate of R0 j 1.45.
We have also used bootstrap methods to estimate the
exponential slope
λ
. This involves selecting random sam-
ples with replacement from the data such that the sample
size equals the size of the actual dataset. The same analy-
sis that was performed on the empirical data is then
repeated on each of these samples. The range of the esti-
mated values
λ
calculated from the random samples
allows determination of the uncertainty in estimation of
λ
. Figure 4 a shows the average
λ
, calculated for different
periods (with abscissa indicating the starting date and the
symbols indicating the duration of the period) from the 5-
day moving average time-series data of infected cases.
The curves corresponding to the periods of different dura-
tions (14–16 days) intersect around 31 July 2009,
indicating that the value of the average exponential slope
is relatively robust with respect to the choice of the
period about this date. The average value of the bootstrap
estimates
λ
at the intersection of the three curves is 0.15,
in agreement with our earlier calculations of
λ
.
Figure 4. a, Averages of the bootstrap estimates for the exponential
slope,
λ
, calculated for different periods (with the abscissa indicating
the starting date and the symbols indicating the duration) from the 5-
day moving average time-series data of infected cases in India. Curves
corresponding to the periods of different durations (14–16 days) inter-
sect around 31 July 2009, indicating that the value of the average expo-
nential slope is relatively robust with respect to the choice of the period
about this date. b, Distribution of bootstrap estimates of the exponential
slope for the period 31 July–15 August 2009. The average slope
λ
obtained from 1000 bootstrap samples is 0.166 with a standard devia-
tion of 0.024, which agrees with the approximate value of
λ
= 0.15
(corresponding to R0 = 1.45) calculated in Figure 3.
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CURRENT SCIENCE, VOL. 100, NO. 7, 10 APRIL 2011
1054
Table 1. Regional variation of basic reproduction number for 2009
influenza A(H1N1)v in India
Region/city Perioda
λ
R0
Pune 30/07–14/08 0.25 ± 0.04 1.74 ± 0.14
Mumbai 05/08–20/08 0.22 ± 0.06 1.65 ± 0.18
Delhi 13/08–28/08 0.12 ± 0.02 1.36 ± 0.06
Southern regionb 15/08–30/08 0.11 ± 0.02 1.34 ± 0.05
R0 is estimated by the method of exponential curve fitting from 5-day
moving averages of incidence data for different regions/cities. In each
case, bootstrap estimates yielded similar values.
aFor each region/city, the time interval over which R0 is determined is
chosen on the basis of exhibiting the highest rise in disease incidence.
bThe Southern region comprises the cities of Bangalore, Chennai and
Hyderabad.
Figure 4 b shows the distribution of the bootstrap esti-
mates of the exponential slope for a particular period, 31
July–15 August 2009. The average slope
λ
obtained
from 1000 bootstrap samples for this period is 0.166 with
a standard deviation of 0.024, which indicates that the
spread of values around the average estimate of
λ
= 0.15
is not large. This confirms the reliability of the estimated
value of the exponential slope, and hence of our calcula-
tion of the basic reproduction number.
In addition to estimating R0 for the entire country, we
have also separately evaluated the basic reproduction
number for the different regions in which the epidemic
occurred (Table 1). It may appear surprising that there
was a large number of infections in Pune (1238 positive
cases up to 30 September), despite it being less well-
connected to the other major metropolitan cities of India,
in comparison to urban centres that did not show a high
incidence of the disease. For example, the Kolkata met-
ropolitan area, which has a population around three times
that of the Pune metropolitan area (http://www.world-
gazetteer.com/; retrieved on 18 February 2010), had only
113 positive cases up to 30 September. This could possi-
bly reflect the role of local climatic conditions: Pune,
located at a relatively higher altitude, has a generally
cooler climate than most Indian cities. In addition, the
close proximity of Pune to Mumbai and the high volume
of road traffic between these two cities could have helped
in the transmission of the disease. Another feature point-
ing to the role of local climate is the fact that in Chennai,
most infected cases were visitors from outside the city,
while in Pune, majority of the cases were from the local
population, even though the total number of infected
cases listed for the two cities in our dataset is comparable
(928 in Chennai and 1213 in Pune). This suggests the
possibility that the incidence of the disease in Pune could
have been aided by its cool climate, in contrast to the hot-
ter climate of the coastal city of Chennai. The rapid
spread of the disease in Pune may also have originated in
transmission amongst the large crowds of people who had
gathered in the H1N1 testing centres, given that the num-
bers appearing for testing here were much larger than
elsewhere.
The calculation of R0 for India assumes well-mixing of
the population (i.e. homogeneity of the contact structure)
among the major cities in India. Given the rapidity of
travel between the different metropolitan areas via air and
rail, this may not be an unreasonable assumption. How-
ever, some local variation in the development of the epi-
demic in different regions can indeed be seen (Figure 1).
Around the end of July, almost all the cities under study
showed a marked increase in the number of infected
cases indicating spread of the epidemic in the local
population. This justifies our assumption of well-mixing
in the urban population over the entire country for calcu-
lating the basic reproduction number.
To conclude, we stress the implications of our finding
that the basic reproduction number for pandemic influ-
enza A(H1N1)v in India lies towards the lower end of the
values reported for other affected countries. This suggests
that season-to-season and country-to-country variations
need to be taken into account to formulate strategies for
countering the spread of the disease. Evaluation of the re-
productive rate, once control measures have been initi-
ated, is vital in determining the future pattern of spread of
the disease.
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ACKNOWLEDGEMENT. We acknowledge the IMSc Complex Sys-
tems project and PRISM, The Institute of Mathematical Sciences,
Chennai for support.
Received 1 June 2010; re-revised accepted 15 December 2010
... The bootstrap approach is based on the construction of artificial data sets from a given collection of real data, by resampling the observations in a manner consistent with the null hypothesis and then to compute the test statistic of interest for each artificial batch [8]. The bootstrap procedure involves choosing random samples (bootstrap sampleX*), with replacement from the given data set X of size n. ...
... Sampling with replacement means that each observation is selected separately at random from the original dataset X. The number of elements in each bootstrap sample X* equals the n number of elements in the original data set [8]. The range of sample estimates enables to establish the uncertainty of the quantity estimated and the accuracy of statistics. ...
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We aim to understand quantitatively how targeted-layered containment (TLC) strategies contain an influenza pandemic in a populous urban area such as Delhi, India using networked epidemiology. A key contribution of our work is a methodology for the synthesis of a realistic individual-based social contact network for Delhi using a wide variety of open source and commercial data. New techniques were developed to infer daily activities for individuals using aggregate data published in transportation science literature in combination with human development surveys and targeted local surveys. The resulting social contact network is the first such network constructed for any urban region of India. This time varying, spatially explicit network has over 13 million people and more than 200 million people-people contacts. The network has several interesting similarities and differences when compared with similar networks of US cities. Additionally, we use a high performance agent-based modeling environment to study how an influenza-like illness would spread over Delhi. We also analyze well understood pharmaceutical and non-pharmaceutical containment strategies, or a combination thereof (also known as TLCs), to control a pandemic outbreak. (i) TLC strategies produce the mildest and most delayed epidemic out-break than any of the individual interventions; (ii) the epidemic dynamics of Delhi appear to be strongly influenced by the activity patterns and the demographic structure of its local residents; and (iii) a high resolution social contact network helps in analyzing effective public health policies. A high resolution synthetic network is constructed based on surveyed data. It captures the underlying contact structure of a certain population and can be used to quantitatively analyze public health policy effectiveness. To the best of our knowledge, this study is the first of its kind in the Indian sub-continent. Copyright © 2015 Elsevier B.V. All rights reserved.
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The susceptible-infected-removed (SIR) and the susceptible-exposed-infected-removed (SEIR) epidemic models with constant parameters are adequate for describing the time evolution of seasonal diseases for which available data usually consist of fatality reports. The problems associated with the determination of system parameters starts with the inference of the number of removed individuals from fatality data, because the infection to death period may depend on health care factors. Then, one encounters numerical sensitivity problems for the determination of the system parameters from a correct but noisy representative of the number of removed individuals. Finally as the available data is necessarily a normalized one, the models fitting this data may not be unique. We prove that the parameters of the (SEIR) model cannot be determined from the knowledge of a normalized curve of "Removed" individuals and we show that the proportion of removed individuals, [Formula: see text], is invariant under the interchange of the incubation and infection periods and corresponding scalings of the contact rate. On the other hand we prove that the SIR model fitting a normalized curve of removed individuals is unique and we give an implicit relation for the system parameters in terms of the values of [Formula: see text] and [Formula: see text], where [Formula: see text] is the steady state value of [Formula: see text] and [Formula: see text] and [Formula: see text] are the values of [Formula: see text] and its derivative at the inflection point [Formula: see text] of [Formula: see text]. We use these implicit relations to provide a robust method for the estimation of the system parameters and we apply this procedure to the fatality data for the H1N1 epidemic in the Czech Republic during 2009. We finally discuss the inference of the number of removed individuals from observational data, using a clinical survey conducted at major hospitals in Istanbul, Turkey, during 2009 H1N1 epidemic.
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As of 12 May 2009, 5,251 cases of the new influenza A(H1N1) have been officially reported to the World Health Organization (WHO) from 30 countries, with most of the identified cases exported from Mexico where a local epidemic has been going on for the last two months. Sustained human-to-human transmission is necessary to trigger influenza pandemic and estimating the reproduction ratio (average number of secondary cases per primary case) is necessary for forecasting the spread of infection. We use two methods to estimate the reproduction ratio from the epidemic curve in Mexico using three plausible generation intervals (the time between primary and secondary case infection). As expected, the reproduction ratio estimates were highly sensitive to assumptions regarding the generation interval, which remains to be estimated for the current epidemic. Here, we suggest that the reproduction ratio was less than 2.2 - 3.1 in Mexico, depending on the generation interval. Monitoring and updating the reproduction ratio estimate as the epidemic spreads outside Mexico into different settings should remain a priority for assessing the situation and helping to plan public health interventions.
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A novel influenza A (H1N1) virus has spread rapidly across the globe. Judging its pandemic potential is difficult with limited data, but nevertheless essential to inform appropriate health responses. By analyzing the outbreak in Mexico, early data on international spread, and viral genetic diversity, we make an early assessment of transmissibility and severity. Our estimates suggest that 23,000 (range 6000 to 32,000) individuals had been infected in Mexico by late April, giving an estimated case fatality ratio (CFR) of 0.4% (range: 0.3 to 1.8%) based on confirmed and suspected deaths reported to that time. In a community outbreak in the small community of La Gloria, Veracruz, no deaths were attributed to infection, giving an upper 95% bound on CFR of 0.6%. Thus, although substantial uncertainty remains, clinical severity appears less than that seen in the 1918 influenza pandemic but comparable with that seen in the 1957 pandemic. Clinical attack rates in children in La Gloria were twice that in adults (<15 years of age: 61%; >/=15 years: 29%). Three different epidemiological analyses gave basic reproduction number (R0) estimates in the range of 1.4 to 1.6, whereas a genetic analysis gave a central estimate of 1.2. This range of values is consistent with 14 to 73 generations of human-to-human transmission having occurred in Mexico to late April. Transmissibility is therefore substantially higher than that of seasonal flu, and comparable with lower estimates of R0 obtained from previous influenza pandemics.
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A new influenza virus emerged in April 2009 and has spread efficiently, prompting the World Health Organization to declare a Phase 6 pandemic alert. In this commentary, I will discuss the biology of influenza viruses in general and the 2009 pandemic virus, especially their epidemiology, transmission, biology and pathogenesis, treatment and vaccines. I will also discuss the outbreak in India and the shameful lack of scientific data from our country.
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Australia was one of the first countries of the southern hemisphere to experience influenza A(H1N1)v with community transmission apparent in Victoria, Australia, by 22 May 2009. With few identified imported cases, the epidemic spread through schools and communities leading to 897 confirmed cases by 3 June 2009. The estimated reproduction ratio up to 31 May 2009 was 2.4 (95% credible interval (CI): 2.1-2.6). Methods designed to account for undetected transmission reduce this estimate to 1.6 (95% CI: 1.5-1.8). Time varying reproduction ratio estimates show a steady decline in observed transmission over the first 14 days of the epidemic. This could be accounted for by ascertainment bias or a true impact of interventions including antiviral prophylaxis, treatment and school closure. Most cases (78%) in the first 19 days in Victoria were under the age of 20 years-old. Estimates suggest that the average youth primary case infected at least two other youths in the early growth phase, which was sufficient to drive the epidemic.
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We use a time dependent modification of the Kermack and McKendrick model to study the evolution of the influenza A(H1N1)v epidemic reported in the Mexico City area under the control measures used during April and May 2009. The model illustrates how the sanitary measures postponed the peak of the epidemic and decreased its intensity. It provides quantitative predictions on the effect of relaxing the sanitary measures after a period of control. We show how the sanitary measures reduced the maximal prevalence of the infected population from 10% to less than 6% of the total population. We also show how the model predicts the time of maximal prevalence and explains the effect of the control measures.
  • R M Anderson
  • R M May
Anderson, R. M. and May, R. M., Infectious Diseases of Humans, Oxford University Press, Oxford, 1992.
Available from: http://mohfw-h1n1.nic.in/documents
[3] World Health Organization, Pandemic (H1N1) on H1N1, 11 April 2010. Available from: http://mohfw-h1n1.nic.in/documents/PDF/Situational UpdatesArchives/april2010/Situational%20Updates%20 on%2011.04.2010.pdf