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Iowa Mumps Epidemic of 2006 : SIR Model

Iowa Mumps Epidemic of 2006 : SIR Model. Courtney St Clair. Mumps. Infectious parotitis Infectious for 8 days: 3 days before symptoms 4 days after symptoms Can lead to: Hearing loss Aseptic meningitis MMR vaccine 95% Effective. Symptoms. Common Symptoms: fever headache

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Iowa Mumps Epidemic of 2006 : SIR Model

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  1. Iowa Mumps Epidemic of 2006 : SIR Model Courtney St Clair

  2. Mumps • Infectious parotitis • Infectious for 8 days: • 3 days before symptoms • 4 days after symptoms • Can lead to: • Hearing loss • Aseptic meningitis • MMR vaccine 95% Effective

  3. Symptoms • Common Symptoms: • fever • headache • swollen salivary glands under jaw • Infrequent Symptom: • sore throat • cough • orchitis (painful swollen testicles 20-30% males who reached puberty)

  4. Iowa Mumps Outbreak • Estimated 200000 people in Iowa were susceptible to Infectious parotitis • Source of outbreak unknown • Epidemic started with a single case before January 1, 2006 • Last case reported September 30, 2006

  5. S(t)= number of susceptible individuals in population at time t I(t)= number of infected individuals in population at time t R(t)= number of recovered individuals in population at time t N= population size s(t)= S(t)/N (susceptible fraction of the population at time t) i(t)= I(t)/N (infected fraction of the population at time t) r(t)= R(t)/N (recovered fraction of the population at time t) S(t) +I(t) + R(t)=N s(t) + i(t) + r(t)=1

  6. t= time in weeks k=fraction of infected group that recovers b=average number of transmission possible from a given infected person in a time period s(t+1)= s(t) – bs(t)I(t) r(t+1)= r(t)+ki(t) i(t+1)= i(t)+bs(t)i(t)-ki(t)=i(t)*(1+bs(t)-k) If k= 8 days ≈ 1 week then i(t+1) becomes much simpler: i(t+1)= i(t)*(1+bs(t)-k) i(t+1)= i(t)*(1+bs(t)-1) i(t+1)= i(t)bs(t) b=i(t+1)/[(i(t)s(t)] b≈1.289

  7. References • Iowa Department of Public Health “Mumps Background” http://www.idph.state.ia.us/adper/common/pdf/mumps/mumps_background.pdf • Iowa Department of Public Health Rev. “Facts Sheet” 4/20/2006 http://www.idph.state.ia.us/adper/common/pdf/epifacts/mumps.pdf • Iowa Department of Public Health Center for Acute Disease Epidemiology “Iowa Mumps Update Through Wednesday, May 10th, 2006” http://www.idph.state.ia.us/adper/common/pdf/mumps/mumps_update_051106.pdf • Iowa Department of Public Health Center for Acute Disease Epidemiology “Iowa Mumps Update Through Saturday, September 30th, 2006” http://www.idph.state.ia.us/adper/common/pdf/mumps/mumps_update_093006.pdf • Iowa Department of Public Health Center Division of Acute Disease Prevention and Emergency Response “Mumps Guideline for Emergency Departments & Health Care Providers” http://www.idph.state.ia.us/adper/common/pdf/mumps/mumps_facts_physicians.pdf • State Library of Iowa, State Data Center Program “Population by Single Year of Age and Sex for Iowa: 2000-2005” http://data.iowadatacenter.org/datatables/State/stagesingleyearbysex20002005.pdf

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