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Characterizing Infectious Disease Outbreaks: Traditional and Novel Approaches

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## Characterizing Infectious Disease Outbreaks: Traditional and Novel Approaches

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**Characterizing Infectious Disease Outbreaks: Traditional**and Novel Approaches Laura F White 15 October 2013**2009 Influenza A H1N1 Pandemic**• H1N1 pandemic first noticed in February in Mexico. • Large outbreak early on in La Gloria-a small village outside of Mexico City. • Studied extensively in the first report on H1N1 (Fraser, Donelly et al. “Pandemic potential of a strain of Influenza (H1N1): early findings”, Science Express, 11 May 2009.)**Example-H1N1 Outbreak**Edgar Hernandez (four years old): first confirmed case**Quantitative Issues**• How do we determine how fast the disease is spreading? • Reproductive number, serial interval • How do we determine how severe the disease is? • Attack rate, case fatality ratio • A topic for another talk! • How do we determine what interventions will be most effective? • Mathematical modeling, network models, etc. • Estimates of severity and transmission by age group**Importance of parameter estimates**• Good information leads to good policy. • School closure is expensive • Important to determine if it will really help. • If R0 < 2, some estimate that Influenza can be controlled. • Information on R0 and the serial interval can give a good picture of how a disease might spread.**Some of the challenges in infectious diseases**• Dependency in the data. • Chain of infection. • Undetected cases. • Asymptomatic, but still infectious. • Unable to detect with existing surveillance. • Need to act fast with little information.**Approaches to estimation**• Classical: Mathematical models • Network models • Statistical approaches**Simple approach**• Assume exponential growth for the first part of an epidemic. • td is the doubling time of the epidemic, D is the average serial interval. Then use the following to solve for R0. • Overly simplistic and sensitive.**Mathematical models**SIR Model Recovered Infected Susceptible (Contact Rate)*(Transmission Probability)Infected 1/(duration of infectiousness) R0=(attack rate)(contact rate)(duration of infectiousness)**Mathematical Models-Uses**• Modeling vaccination programs • Determining optimal intervention strategies for halt or control an epidemic • HIV transmission routes • Estimating parameters of disease**Mathematical Models: Limitations**• Make a lot of assumptions. • Must plug in a lot of values in order to get estimates. • Do not allow for randomness in processes-always gives a number as the answer with no error bounds. • Stochastic epidemic model. • Can oversimplify the problem. • Challenge to achieve balance between making the model too simple and too complex.**References**• Hethcote • TheMathematicsofInfectiousDiseases. Herbert W. Hethcote. SIAM Review, Vol. 42, No. 4, 599-653. Dec., 2000. • Anderson and May • Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, 1992.**Wallinga & Tuenis**• Network based method to estimate the reproductive number each day of an epidemic. • Requires knowledge of the serial interval. • Requires that all cases have been observed and epidemic is over. • Originated to analyze SARS. American Journal of Epidemiology, 2004**= infected person**Day 1 Day 2 Day 3 Day 4 Day 5 Day 6**Day 1**All possible infectors. Day 2 Day 3 Day 4 Day 5 Day 6**j**Day 1 pt=probability of being infected by a case that appeared t days prior. p3 Day 2 p2 Day 3 p1 p1 p1 p1 i Day 4 Day 5 Day 6**Wallinga & Teunis**• If g(t) is the distribution of the serial interval, then, the relative probability that case i has been infected by case j is: • The effective reproductive number for cases on day j is then:**White & Pagano**• Statistical method, using probability models to estimate the serial interval and reproductive number. • Assume that we observe daily counts of new cases: . • Let Xij be the number of cases with symptoms on day j that were infected by a case with symptoms on day i. Statistics in Medicine, 2008**Method**• Using this scheme, we make some probabilistic assumptions and get a likelihood equation: • Where • pj describes the serial interval (i.e. probability of having symptoms j days after infector). • Use numerical methods to get MLEs of Ro and p.**H1N1 Example**• In April the public became aware of a novel strain of Influenza that was affecting Mexico. • Fraser, Donelly et al published initial report in Science on 11 May 2009. • Estimate the reproductive number to be between 1.4 and 1.6. • Estimate the average serial interval to be 1.91 days.**H1N1 Example**• We obtained data from the CDC with information on each confirmed and suspected case (1368 cases) as of May 8. • 750 had a date of symptom onset.**Influenza A/H1N1: Serial Interval**• Spanish work estimate average serial interval to be 3.5 days, range=1-6 days. • Use contact tracing data. • Seasonal influenza (Cowling et al, 2009) • 3.6 days, SD=1.6 • From a household contact study**Influenza A/H1N1: R0 estimates**• Mexico: 1.3-1.4 (Cruz-Pacheco et al) • Mexico: less than 2.2-3.1 (Boelle et al) • Japan: 2.3 (Nishiura et al) • Netherlands: less than 1 (Hahne et al) • US: 1.7-1.8 (White et al)**Influenza A/H1N1: USA**• Missing dates of symptom onset • All cases have report date but many lack date of symptom onset. • Calculate the distribution of time between reported date and symptom onset for those with both. • Impute a date of symptom onset for those with missing information from the observed distribution.**Other issues in the data**• Imported cases • Make an adjustment in the estimation method to account for those who were known to have traveled to Mexico. • Reporting delay • The decline in cases as it gets closer to May 8 is likely due to reporting delays, rather than a true drop off in case numbers. • Augment the data at the end, using the reporting delay distribution.**Estimates in the USA**• Using the White & Pagano Method with the modifications mentioned we get estimates for R0 and the serial interval in the initial outbreak in the US.**Serial interval estimate**Using data up to and including April 25, 2009. Using data up to and including April 27, 2009.**Heterogeneity**• Variation in transmission between adults and kids, geographically, etc. • Can lead to better policy decisions • Who gets vaccinated first? • Social distancing measures that might be most effective?**Overview**• Social mixing matrices • Glass method • Modification of Wallinga and Teunis • Modification of White and Pagano**Social mixing**• To understand who is most culpable for transmission, we typically need to understand how people interact • Many approaches to this, but we choose most popular currently: social mixing matrices**PolyMod study**• Large European study • Belgium, Finland, Great Britain, Germany, Italy, Luxembourg, the Netherlands, and Poland • 97,904 contacts among 7,290 participants • Participants record number and nature of contacts in a diary • Contact matrices were created to describe all close contacts and separately, close contacts that involve physical touch**Table 1.**Mossong J, Hens N, Jit M, Beutels P, et al. (2008) Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases. PLoS Med 5(3): e74. doi:10.1371/journal.pmed.0050074 http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0050074**Figure 1. The Mean Proportion of Contacts That Involved**Physical Contact, by Duration, Frequency, and Location of Contact in All Countries Mossong J, Hens N, Jit M, Beutels P, et al. (2008) Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases. PLoS Med 5(3): e74. doi:10.1371/journal.pmed.0050074 http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0050074**Figure 2. The Distribution by Location and by Country of (A)**All Reported Contacts and (B) Physical Contacts Only Mossong J, Hens N, Jit M, Beutels P, et al. (2008) Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases. PLoS Med 5(3): e74. doi:10.1371/journal.pmed.0050074 http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0050074**Figure 3. Smoothed Contact Matrices for Each Country Based**on (A) All Reported Contacts and (B) Physical Contacts Weighted by Sampling Weights Mossong J, Hens N, Jit M, Beutels P, et al. (2008) Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases. PLoS Med 5(3): e74. doi:10.1371/journal.pmed.0050074 http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0050074**Other studies**Similar studies have been conducted in South Africa and Vietnam First of this nature in Netherlands (Wallinga et al, 2006) Johnstone-Robertson et al (2011) carried out a very similar study in a South African township**Approaches**• Glass et al, 2011 • Estimate R for adults and children • Do not require transmission data • Modify Wallinga and Teunis method • Estimate Rt (and R0) across age groups. • Require contact information. • Moser and White, 2013 (in preparation) • Bayesian approach to the problem • Modify White & Pagano method to incorporate age contact information • Incorporate contact information as a prior distribution**Approach 1: Glass et al**M= Modify Wallinga & Teunis and White & Pagano methods to estimate R for children and adults Assume a form for a reproduction matrix: mijdescribes the number of cases of type i infected by cases of type j. Some pre-specified structure must be imposed on the matrix M must be assumed to estimate the mij.**Matrix constraints**Source: Glass et al, 2011