Case study: Epidemic modelling in real life Epidemic modelling, simulation and statistical analysis Stockholm 2015. Sharon Kühlmann-Berenzon 2015-11-09
Outline for the day 1.Epidemic modelling: what is it for, extension, real life 2.Ebola case study Background on Ebola outbreak 2014 Deterministic modeling Stochastic modeling 3.Beyond modelling <Lunch> 4.Classroom exercises: mental modeling and conceptualization In groups Paper and pen Oral presentation Sid.
1. Epidemic modelling: what is it good for for? All models are wrong but some are useful. (Box, 1979) 1.Understand mechanisms of the spread What are key factors speeding/breaking the spread Human contact, international travel, mass movement 2.Control: how, what intervention is more effective Plan interventions Optimize interventions 3.Prediction, preparedeness Can it happen again? What are realistic scenarios? Burden and consequences in society Preventive measures Sid.
Extensions to the SIR model Sid.
Basic reprodcution number: R 0 Disease Transmission R 0 Measles Airborne 12 18 Pertussis Airborne droplet 12 17 Wikipedia, 20120920 Sid. Diphtheria Saliva 6 7 Smallpox Social contact 5 7 Polio Fecal-oral route 5 7 Rubella Airborne droplet 5 7 Mumps Airborne droplet 4 7 HIV/AIDS Sexual contact 2 5 SARS Airborne droplet 2 5 Influenza (1918 pandemic strain) Airborne droplet 2 3
Real life applications Pandemic influenza 2009: possible scenarios for health care and vital services, vaccination strategy, R 0 UK food-and-mouth outbreak 2001: vaccination strategy, preparedeness for future outbreak by understanding spread of the disease Dengue in Taiwan: understanding effect of temperature, preparedeness HIV and XDRTB: understand interaction for control measures of TB Cost-effectiveness of Chlamydia systematic screening in the Netherlands: predict epidemic and other outcomes as input in a cost analysis Outbreak in camel population of unknown aethiology: Understand spread and possible key factors Sid.
2. Ebola virus (EBV) Viral disease (Filoviridae family). Transmitted from wild animals to humans, direct human-to-human contact (blood, broken skin, mucous membranes, organs, bodily fluids). Unknown until 1976, simultaneously identified in Sudan and Democratic Republic of Congo (Ebola river). Incubation time: 2-21 days; infectious when symptomatic. Symptoms: sever fatigue, muscle pain, headache, sore throat; vomitting, diarrhoea, rash, symptoms of impaired kidney and liver function, internal and external bleeding. Difficult to distinguish from malaria, typhoid fever, meningitis. No proven treatment nor vaccine. Source: WHO, http://www.who.int/mediacentre/factsheets/fs103/en/ Sid.
Year Country Ebolavirus species Cases Deaths Case fatality 2012 Democratic Republic of Congo Bundibugyo 57 29 51% Previous Ebola outbreaks 2012 Uganda Sudan 7 4 57% 2012 Uganda Sudan 24 17 71% 2011 Uganda Sudan 1 1 100% 2008 Democratic Republic of Congo Zaire 32 14 44% 2007 Uganda Bundibugyo 149 37 25% 2007 Democratic Republic of Congo Zaire 264 187 71% 2005 Congo Zaire 12 10 83% 2004 Sudan Sudan 17 7 41% 2003 (Nov-Dec) Congo Zaire 35 29 83% 2003 (Jan-Apr) Congo Zaire 143 128 90% 2001-2002 Congo Zaire 59 44 75% 2001-2002 Gabon Zaire 65 53 82% 2000 Uganda Sudan 425 224 53% 1996 South Africa (ex-gabon) Zaire 1 1 100% 1996 (Jul-Dec) Gabon Zaire 60 45 75% 1996 (Jan-Apr) Gabon Zaire 31 21 68% 1995 Democratic Republic of Congo Zaire 315 254 81% 1994 Cote d'ivoire Taï Forest 1 0 0% 1994 Gabon Zaire 52 31 60% 1979 Sudan Sudan 34 22 65% 1977 Democratic Republic of Congo Zaire 1 1 100% 1976 Sudan Sudan 284 151 53% 1976 Democratic Republic of Congo Zaire 318 280 88% Sid 8. Source: WHO. http://www.who.int/mediacentre/factsheets/fs103/en/
Ebola Virus Disease Distribution Map CDC,http://www.cdc.gov/vhf/ebola/outbreaks/history/d istribution-map.html Sid 9.
Ebola outbreak 2014: Timeline Dec, 2013: Suspected index case, 2-year old, dies in Guinea. Spread continuos as disease is not recognized and in the context of a poor public health system. March 2014: Guinea reporting a mysterious hemorrhagic fever. From Jan 14, 87 cases, 61 deaths. Ebola confirmed. Liberia confirmed cases and Sierra Leone suspected cases. April, 2014: MSF warns Ebola s spread as unprecedented. May 2014: Sierra Leone reports first deaths. June 2014: Liberia reports cases in its capital, Monrovia. July 2014: Spread in Nigeria by a Liberian-American women arriving by plane in Lagos. August 2014: WHO declares the epidemic a public health emergency of international concern. Seven African countries close their borders with affected countries. September 2014: Sierra-Leone sets almost a third of population in quarantine. October 2014: WHO estimates 3,388 deaths out of 7,178 cases. First case in Mali. Senegal and Nigeria declared EBV free. November 2014: According to WHO 5,160 deaths out of 14,098 cases. Sid.
Ebola outbreak 2014 (cont) January 2015: Mali-government declares Ebola free. May 2015: Liberia declared Ebola free. June 2015: Ebola returns to Liberia. July 2015: Cases in Liberia, Guinea, Sierra Leone. September 2015: Liberia Ebola free. October 2015: New cases in Guinea. As of 2 Nov 2015: 28,514 cases, 11,313 deaths www.scientificamerican.com, www.abc.news.au, www.livescience.com, apps.who.int, msf.org Sid 11.
Epidemic curve: July/2014-March/2015 "West Africa Ebola 2014 13 Reported Cases per Week" by Malanoqa - Own work. https://commons.wikimedia.org/wiki/file:west_africa_ebola_2014_13_reported_cases_per_week.png#/media/file:west_afr Sid. ica_ebola_2014_13_reported_cases_per_week.png
"West Africa Ebola 2014 6 cum case by country log" by Malanoqa https://commons.wikimedia.org/wiki/file:west_africa_ebola_2014_6_cum_case_by_country_log.png Sid 13.
Situation map of the outbreak in West Africa updated 2015-10-28 Source: https://upload.wikimedia.org/wikipedia/commons/thumb/8/81/2014_ebola_virus_epidemic_in_west_africa_ simplified.svg/1280px-2014_ebola_virus_epidemic_in_west_africa_simplified.svg.png Sid.
Published epidemic modelling studies of Ebola outbreak 2014 since Sept 2014 Estimate R 0 Size of outbreak Number of treatment centers (beds) needed Effect of increase in case ascertainment Efficacy of protective kits Effect of contact tracing Effect of traditional practices in spread Effect of behaviour changes Change in date of start of intervention Epidemic dynamics in hospital staff and general population Impact of vaccination: timing, strategy Economic cost Risk for import to unaffected areas Sid 15.
Case Study: Rivers et al, Oct 2014 Aim: Describe development of the outbreak Short term projections Potential impact of: contact tracing, improved access to PPE, Pharmaceutical intervention How: a. Deterministic model b. Stochastic model Sid.
Deterministic model Susceptible Exposed Infectious Funeral Hospitalized Removed/ Recovered Sid.
Deterministic model - reformulated 2a. Deterministic model Sid 18.
Differential equations Sid 19.
Deterministic model: calibration up to the present (Oct 2014) Calibration to by least-squares optimization. Last 15 days were given w=0,24 due to improved reporting. Parameter constraints. Candidate fitted models were ¼ contact with hospitalized patients, ¼ from funeral, ½ from person-to-person contact in the community -> anectdotal reports. Sid 20.
Stochastic model for prediction Implemented with Gillespie tau-algorithm; individual-based, random time-steps, deterministic rates assumed as probabilities; from calibrated-deterministic model: start with n in each compartment, and estimated parameters; time horizon from Oct - 31 Dec 2014; 250 simulations (uncertainty in predictions). Sid 21.
Stochastic model: scenarios a. Improved contact tracing increase proportion cases hospitalized and decrease in time for a case to be hospitalized. b. Decrease contact rate in hospital ( increase use of PPE and awareness); and eliminate post-mortem infection from hospitalized cases. c. Decrease contact rate in hospital and eliminate post-mortem infection; and increase in proportion of hospitalized cases. d. Pharmaceutical intervention that increases survival of hospitalized cases. Sid 22.
Deterministic model: Fitted parameters Sid 23.
Model fit and prediction: Liberia Sid 24.
Model fit and prediction: Sierra Leone Sid 25.
Liberia: a) increased contact tracing Community Hospitalized Funeral Total Contact Trace Baseline 80% 90% 100% R0 2,22 2,11 2,01 1,89 Sid 26.
Liberia: b) decrease hospital transmission and no post-mortem infection Community Hospitalized Funeral Total Sid 27. Hosp transmission Baseline 25% 50% 75% R0 2,22 2,13 2,05 1,96
Liberia: c) decrease hospital transmission and increase contact traced (median cases decrease vs baseline) Community Hospitalized % contact traced Funeral Total Sid 28. % decrease hosp transmission
Conclusion No intervention studied will stop the epidemic. In best case it will slow down. Limitations: Data used is dated by report-date, not onset. Therefore accuracy of the model is difficult to assess. Strengths: Uncertainty in future predictions is quantified by using stochastic simulation (vs deterministic). Sid 29.
Beyond the modeling Disease: epidemiology, clinical picture, clinical course. What is the question. Data: what is available, quality, accuracy, specificity, sensitivity. Calibration of model to data. Measure uncertainty: sensitivity analysis, confidence intervals. Strengths and limitations of conceptualization, implementation, assumptions, inference. IT S A MULTIDISCIPLINARY ENDEAVOUR! Sid 30.
Minnesota Health #3: I think we need to consider closing schools down. Minnesota Health #4: And who stays home with the kids? People that work on stores, government workers, people that work in hospitals. When will we know what this is? What causes it? What cures it? Things to keep people calm. Dr. Erin Mears: What we need to determine is this; for every person who gets sick, how many other people are they likely to infect? So, for seasonal flu that's usually about one. Smallpox on the other hand, it's over three. Now, before we had vaccine, Polio spread at a rate between four and six. Now, we call that number the R-not. R stands for the reproductive rate of the virus. Minnesota Health #3: Any ideas what that might be for this? Dr. Erin Mears: How fast it multiplies depends on the variety of factors; the incubation period, how long a person is contagious. Sometimes people can be contagious without even having symptoms, you need to know that too. And we need to know how big the population of people susceptible to the virus might be. Minnesota Health #4: So far that appears to be everyone with hands, a Sid. mouth and a nose.
3. Classroom exercise: Mental model Purpose: choose one or several objectives for the model (Mechanism, Control, Preparedness) Stochastic vs Deterministic: which and why Conceive and sketch a mental/conceptual model Data: what is needed, how to get it Limitations: what is not accounted for, what has been simplified Present max 10 min Use internet as needed (eg. Wikipedia, CDC.gov) Sid.
Outbreaks 1.MRSA in a hospital 2.Cholera in a refugee camp 3.Mutation of Chlamydia bacteria goes undetected in the lab (false negatives) 4.Vector-borne disease (malaria, dengue, West Nile) Sid.
Back to Ebola How would you improve or modify the epidemic model by Rivers et al? Interventions: contact tracing, hospital transmission, funeral, medical treatment. Sid 34.
4. Links R and compartmental models: Play with parameters, see results in S-I-R model: Rivers-etal, PLOS Current Outbreaks, 6 Nov 2014 http://sherrytowers.com/2012/12/11/simple-epidemic-modellingwith-an-sir-model/#numeric https://www.khanacademy.org/science/health-and-medicine/currentissues-in-health-and-medicine/ebola-outbreak/p/modelling-anepidemic http://currents.plos.org/outbreaks/article/modeling-the-impact-ofinterventions-on-an-epidemic-of-ebola-in-sierra-leone-and-liberia/ Sid 35.