Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Melanie Payton - North Carolina Agricultural and Technical State University
Co-Author(s): Liping Liu, Lauren Davis, and Gouqing Tang, North Carolina Agricultural and Technical State University, Greensboro, NC
The measles is a highly contagious vaccine preventable disease caused by a virus. In recent years, the national and state vaccination rates of measles remain high, thus the United States declared that measles was eliminated. However, recent news has shown several outbreaks, which may be due to pockets of low vaccination coverage. This study focuses on the dynamics of the measles spread, in particular the impact of the pockets of low vaccination coverage.
Based on the generic spatial model of Lloyd and May (Lloyd & May, 1996), a deterministic spatial S-V-I-R (Susceptible-Vaccinated-Infected-Recovered) model is developed for a number of regions with various vaccination coverage. The parameters are estimated from various data sources. The differential equations model is coded into a Matlab program. The mathematical analysis for the reproductive number is conducted to analyze the impacts of low/high vaccination communities.
Numerous numerical simulations and mathematical analysis on the reproductive numbers reveal that: 1) the existence of low vaccinated communities increases the total number of infected individuals; 2) the proportion of low vaccinated communities plays a role in the spread of the measles. The results show that the state and national vaccination coverage can be misleading, and that there can be different configurations with smaller communities that do not change the average but drastically change the spread of measles.
Furthermore, in the event of an outbreak, a food distribution model is developed to deliver food from the Federal Emergency Management Agency food banks to communities affected by the measles. The objective is to minimize unit-shipping costs while satisfying demand (the number of infected individuals).
In future work, we will extend the current spatial SVIR model to include other factors such as age dependence and seasonality to investigate the long-term effects. We will develop a stochastic simulation model for the communities with high/low vaccination coverage. We will extend the food distribution model to include relevant medical supplies. Lastly, we will continue contributing to the applied math and humanitarian logistics specialty.
Key Reference: Lloyd, Alun L, & May, Robert M. (1996). Spatial heterogeneity in epidemic models. Journal of theoretical biology, 179(1), 1-11.ERN abstract Oct 2.docx
Funder Acknowledgement(s): This research is supported by The Louis Stokes Alliances for Minority Participation (LSAMP) Bridge to Doctorate Program.
Faculty Advisor: Liping Liu, firstname.lastname@example.org