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Ordinary Differential Equations and Applied Dynamics Commons™
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Articles 1 - 4 of 4
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Nonsmooth Epidemic Models With Evolutionary Game Theory, Cameron Morin
Nonsmooth Epidemic Models With Evolutionary Game Theory, Cameron Morin
Electronic Theses and Dissertations
This thesis explores the utilization of game theory and nonsmooth functions to enhance the accuracy of epidemiological simulations. Traditional sensitivity analysis encounters difficulties when dealing with nondifferentiable points in nonsmooth functions. However, by incorporating recent advancements in nonsmooth analysis, sensitivity analysis techniques have been adapted to accommodate these complex functions. In pursuit of more accurate simulations, evolutionary game theory, primarily the replicator equation, is introduced, modeling individuals’ decision making processes when observing others’ choices. The SEIR model is explored in depth, and additional complexities are incorporated, leading to the creation of an expanded SEIR model, the Be-SEIMR model.
Computationally Modeling Dynamic Biological Systems, Katherine Jarvis
Computationally Modeling Dynamic Biological Systems, Katherine Jarvis
Electronic Theses and Dissertations
Modeling biological systems furthers our understanding of dynamic relationships and helps us make predictions of the unknown properties of the system. The simple interplay between individual species in a dynamic environment over time can be modeled by equation-based modeling or agent- based modeling (ABM). Equation based modeling describes the change in species quantity using ordinary differential equations (ODE) and is dependent on the quantity of other species in the system as well as a predetermined rates of change. Unfortunately, this method of modeling does not model each individual agent in each species over time so individual dynamics are assumed to …
Lexicographic Sensitivity Functions For Nonsmooth Models In Mathematical Biology, Matthew D. Ackley
Lexicographic Sensitivity Functions For Nonsmooth Models In Mathematical Biology, Matthew D. Ackley
Electronic Theses and Dissertations
Systems of ordinary differential equations (ODEs) may be used to model a wide variety of real-world phenomena in biology and engineering. Classical sensitivity theory is well-established and concerns itself with quantifying the responsiveness of such models to changes in parameter values. By performing a sensitivity analysis, a variety of insights can be gained into a model (and hence, the real-world system that it represents); in particular, the information gained can uncover a system's most important aspects, for use in design, control or optimization of the system. However, while the results of such analysis are desirable, the approach that classical theory …
An Epidemiological Model With Simultaneous Recoveries, Ariel B. Farber
An Epidemiological Model With Simultaneous Recoveries, Ariel B. Farber
Electronic Theses and Dissertations
Epidemiological models are an essential tool in understanding how infection spreads throughout a population. Exploring the effects of varying parameters provides insight into the driving forces of an outbreak. In this thesis, an SIS (susceptible-infectious-susceptible) model is built partnering simulation methods, differential equations, and transition matrices with the intent to describe how simultaneous recoveries influence the spread of a disease in a well-mixed population. Individuals in the model transition between only two states; an individual is either susceptible — able to be infected, or infectious — able to infect others. Events in this model (infections and recoveries) occur by way …