Mathematical Modeling Of Influenza At Penn State: a Study Of Incidence Patterns And Effect Of Vaccination
Open Access
- Author:
- Inciardi, Allegra Marie
- Area of Honors:
- Mathematics
- Degree:
- Bachelor of Science
- Document Type:
- Thesis
- Thesis Supervisors:
- Timothy Charles Reluga, Thesis Supervisor
Victoria V Sadovskaya, Thesis Honors Advisor - Keywords:
- influenza
mathematical model
influenza vaccination - Abstract:
- Every year, influenza strikes University Park and affects the student body. This project in mathematics looks at the nature of the infectious disease as it travels through the student body, paying particular attention to incidence rates. In addition, the school vaccination policy is analyzed to see how it affects the incidence rate of cases of influenza. Data was obtained from Penn State University Student Health Services in the form of new cases of influenza per week over the past 5 years. Mathematical models, primarily differential equations, were used to discover how severe the influenza outbreaks at Penn State have been. The Kermack – McKendrick Simple Model was used to obtain a set of parameters to graphically model the data. The parameters obtained produced the basic reproductive number (R0). R0 is defined as the average number of secondary cases from one primary case. This measures how severe the outbreak was. The data showed that there have been influenza outbreaks in all of the past 5 years, and four of these have been epidemics. The outbreak was categorized as an epidemic if the UHS Rate of Influenza-like-illness surpassed the PA Baseline influenza rate. The R0 values were, in chronological years, 2.8, 2.0, 1.2, 1.8, and 1.45. A minimization was done for each year to verify that it was correct to vary the transmission rate from year to year. The minimization showed that each outbreak has unique parameters, instead of one set of parameters to model every outbreak. Simulations showed that outbreaks were not dependent on outbreaks from previous years. Vaccinating students reduced the number of susceptible students, thus reducing R0 and making the epidemic less severe. The number of students vaccinated corresponded approximately linearly to the reduction in number of students being infected until the outbreak was over.