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 –swollen salivary glands under jaw Infrequent Symptom: –sore throat –cough –orchitis (painful swollen testicles 20-30% males who reached puberty)

Iowa Mumps Outbreak Estimated 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

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

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

References Iowa Department of Public Health “Mumps Background” pdf pdf Iowa Department of Public Health Rev. “Facts Sheet” 4/20/ Iowa Department of Public Health Center for Acute Disease Epidemiology “Iowa Mumps Update Through Wednesday, May 10th, 2006” pdf pdf Iowa Department of Public Health Center for Acute Disease Epidemiology “Iowa Mumps Update Through Saturday, September 30th, 2006” pdf pdf Iowa Department of Public Health Center Division of Acute Disease Prevention and Emergency Response “Mumps Guideline for Emergency Departments & Health Care Providers” ans.pdf ans.pdf State Library of Iowa, State Data Center Program “Population by Single Year of Age and Sex for Iowa: ” pdf pdf