Theses and Dissertations

Date of Award


Document Type


Degree Name

Master of Science (MS)



First Advisor

Dr. Erwin Suazo

Second Advisor

Dr. Tamer Oraby

Third Advisor

Dr. Zhijun Qiao


Reaction-diffusion equations are nonlinear partial differential equations that have been used extensively in mathematical modeling. An interesting case in this type of equation is the Fisher-Kolmogorov system, which has been used to study a low-grade glioma, a group of primary brain tumors. In the first part of this thesis, a stochastic version of the Fisher-Kolmogorov system will be studied, and exact and numerical solutions will be presented.

The second part of this thesis will show how the speed of information propagation affects disease spread and vaccination uptake through networks in epidemics. In this model, the information reaches different people at different distances from the center of information containing the health data. The Fisher-Kolmogorov equations are used to depict the vaccine and disease information propagation on a network embedded into a straight line. The Fisher-Kolmogorov equations are coupled equations with the SIR (Susceptible-Infected-Recovered) model to examine the anticipated mutual influence. Numerical simulations of the model are presented. It is shown how the propagation of information about the disease impacts the probability of vaccination and, consequently, the vaccination rate.


Copyright 2020 Juan J. Huerta. All Rights Reserved.

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