Mathematical Modeling of Potassium Modulated Viral Infection
In recent years, there is a growing interest in the investigation of using potassium to treat virus infections. In the region of infection, there is a biological observation of extracellular potassium level being typically very low whereas the intracellular potassium levels are much higher. There are numerous biological studies showing that elevated potassium levels in the extracellular membrane tends to block virus infections. A recent effort in this direction is a collaborative research conducted by mathematicians and biologists from the University of Texas at El Paso, New Mexico State University, and the University of New Mexico, where we develop a mathematical model that demonstrates the blocking effect extracellular potassium has on the Myxoma virus in rabbits. In this thesis, we will conduct preliminary analysis of the mathematical model proposed in this project, with an emphasis on answering the question whether this model is capable of predicting the potassium blocking effect on virus infections at all. More specifically, this model is composed of a system of parameterized ordinary differential equations for various cell number densities and reaction-diffusion equations for virus and potassium concentrations. Particularly for the latter, we establish lower and upper bounds for the virus and potassium concentrations using a comparison principle, and show that the model admits positive and thus biological relevant solutions. Furthermore, the upper bounds are given in closed-form expression of model parameters and they help us provide an affirmative answer to the fundamental question raised before. Such a positive answer motivates the implementation of a computational method for the numerical simulation of the model, and we present some simulation results confirming our prediction in the last part of the thesis.
Mathematics|Biology|Virology|Bioinformatics|Applied Mathematics|Physical chemistry
Mather, Zaira Elizabeth, "Mathematical Modeling of Potassium Modulated Viral Infection" (2022). ETD Collection for University of Texas, El Paso. AAI29211734.