Dr. Pamela Pyzza (Department of Mathematics and Computer Science, Neuroscience Program)

Diseases such as HIV, HPV, TB, and influenza, are all spread from one individual to another and can cause an epidemic if not properly contained and vaccinated against. The key to the spread of these diseases is human contact, as viruses like HIV and HPV are transmitted primarily through sexual contact [1,2], while TB and the flu are transmitted to people nearby through the air [3].

One approach to mathematically modeling the spread of and vaccination against such diseases uses agent-based modeling and focuses on basic social network structures [4]. Agent-based modeling allows us to model individual people and connect them in various network structures to form a community [5]. The individuals or agents in the model have various traits that make them unique. They are connected by edges or links, across which the disease may transmit. According to an established set of rules, stochastic random processes determine which edges are active at a particular time.

The necessary details about people and their interactions are specific to the particular disease being studied. For example, when modeling the spread of HPV, an individual’s age and gender are important [6], while contracting the flu is more dependent on where an individual spends most of their time.

Students will conduct literature searches to obtain current details about the disease, its means of transmission, and any possible vaccination methods that may exist. They will implement an agent-based model for the spread of a disease using MATLAB or C++, comparing their results with data from the CDC and other health databases. They can use their models to begin to ask and answer questions which are otherwise not feasible, unethical, or too expensive to test on humans. Given a model describing the spread of a disease, additional stochastic processes can be incorporated to model the vaccination of individuals against the disease [6–8]. Students can develop various vaccination policies for eradicating the disease and use their model to test the efficacy of each methods.

References

[1] Center for Disease Control and Prevention, Sexually Transmitted Disease Surveillance 2013. Atlanta: U.S. Department of Health and Human Services, Dec. 2014.

[2] M.-C. Boily, G. Godin, M. Hogben, L. Sherr, and F. I. Bastos, “The impact of the transmission dynamics of the hiv/aids epidemic on sexual behaviour: a new hypothesis to explain recent increases in risk taking-behaviour among men who have sex with men,” Med. Hypotheses 65, pp. 215–226 (2005).

[3] Y.-H. Cheng, C.-H. Wang, S.-H. You, N.-H. Hsieh, W.-Y. Chen, C.-P. Chio, and C.-M. Liao, “Assessing coughing-induced influenza droplet transmission and implications for infection risk control,” Epidemiol. Infect., pp. 1–13 (2015).

[4] L. Perez and S. Dragicevic, “An agent-based approach for modeling dynamics of conta­gious disease spread,” Int. J. Health. Geogr. 8, p. 50 (2009).

[5] X. Fu, M. Small, D. M. Walker, and H. Zhang, “Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization,” Phys. Rev. E 77, 036113 (2008).

[6] Center for Disease Control and Prevention, “Genital hpv infection -fact sheet.” [http://www.cdc.gov/STD/HPV/STDFact-HPV.htm].

[7] E. Herweijer, A. L. Feldman, A. Ploner, L. Arnheim-Dahlstrom, I. Uhnoo, E. Netterlid, J. Dillner, P. Sparen, and K. Sundstrom, “The participation of hpv-vaccinated women in a national cervical screening program: Population-based cohort study,” PLoS One 10, p. e0134185 (2015).

[8] A. L. Greer, “Early vaccine availability represents an important public health advance for the control of pandemic influenza,” BMC Res. Notes 8, p. 191 (2015).