Compartmental Measles Modeling for Subgroup Populations

open_access
Open Access
Author:
Black, Elizabeth
Area of Honors:
Mathematics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
Jessica Maral Conway, Thesis Supervisor
Victoria V Sadovskaya, Thesis Honors Advisor
Keywords:
SIR Model
Stochastic Model
Epidemic Modeling
Abstract:
Most epidemic modeling focuses on the big, faraway populations and outbreaks, and how an outbreak in one population affects the other. There is little to no epidemiological modeling focused on specific subgroups in a population and their effects on each other. The purpose of this paper is to explore how individual subgroups' interactions in a population can affect an outbreak. We first started by creating a simple SIR model for this scenario, finding the parameters, and deriving the equation $R_0$. Then, we ran some simulations to gain a better understanding of the model. After this, we converted the general SIR model to a Stochastic model to account for the randomness of individual interactions and ran some simulations. We found that, depending on the rate of interaction between the two subgroups and vaccination percentages of the subgroups, it had a big impact on whether there would be an outbreak in the total population. We also found that it impacted whether the subgroups would experience an outbreak. Further research on this base model could be done to explore how this works in real-world scenarios. The model could also be made more accurate if further research were done on unknown parameters, and, if there is enough data on real-world scenarios, data fitting could be performed.