Optimal Control Applied to Population and Disease Models

This dissertation considers the use of optimal control theory in population models for the purpose of characterizing strategies of control which minimize an invasive or infected population with the least cost. Three different models and optimal control problems are presented. Each model describes population dynamics via a system of differential equations and includes the effects of one or more control methods. The first model is a system of two ordinary differential equations describing dynamics between a native population and an invasive population. Population growth terms are functions of the control, constructed so that the value of the control may affect each population differently. A novel existence result is presented for the case of quadratic growth functions. With parameters chosen to mimic the competition between cottonwood and salt cedar plants, optimal schedules of controlled ooding are displayed. The second model, a system of six ordinary differential equations, describes the spread of cholera in a human population through ingestion of Vibrio cholerae. Equations track movement of susceptible individuals to either an asymptomatic infected class or a symptomatic infected class through ingestion of bacteria, both in a hyperinfectious state and a less-infectious state. Recovered individuals temporarily move to an immune class before being placed back in the susceptible class. A new result quantities contributions to the basic reproductive number from multiple infectious classes. Within the model, three control functions represent rehydration and antibiotic treatment, vaccination, and sanitation. The cost-effective balance of multiple cholera intervention methods is compared for two endemic populations. The third model describes the spread of disease in both time and space using a system of three parabolic partial differential equations with convection-diffusion movement terms and no-flux boundary conditions. A control function representing vaccination is incorporated. State variables track the number of susceptible, infected, and immune individuals. Detailed analysis for the characterization of the optimal control is provided. The model and optimal control results are applied to the spread of rabies among raccoons with the control function determining the timing and placement of oral vaccine baits. Results illustrate cost-effective vaccine distribution strategies for both regular and irregular patterns of rabies propagation

Modeling Neural Behavior and Pain During Bladder Distention using an Agent-based Model of the Central Nucleus of the Amygdala

Chronic bladder pain evokes asymmetric behavior in neurons across the left and right hemispheres of the amygdala. An agent-based computational model was created to simulate the firing of neurons over time and in response to painful bladder stimulation. Each agent represents one neuron and is characterized by its location in the amygdala and response type (excited or inhibited). At each time step, the firing rates (Hz) of all neurons are stochastically updated from probability distributions estimated from data collected in laboratory experiments. A damage accumulation model tracks the damage accrued by neurons during long-term, painful bladder stimulation. Emergent model output uses neural activity to measure temporal changes in pain attributed to bladder stimulation. Simulations demonstrate the model\u27s ability to capture acute and chronic pain and its potential to predict changes in pain similar to those observed in the lab. Asymmetric neural activity during the progression of chronic pain is examined using model output and a sensitivity analysis

Modeling the Population Effects of Hypoxia on Atlantic Croaker (Micropogonias undulatus) in the Northwestern Gulf of Mexico: Part 2—Realistic Hypoxia and Eutrophication

Quantifying the population-level effects of hypoxia on coastal fish species has been challenging. In the companion paper (part 1), we described an individual-based population model (IBM) for Atlantic croaker in the northwestern Gulf of Mexico (NWGOM) designed to quantify the long-term population responses to low dissolved oxygen (DO) concentrations during the summer. Here in part 2, we replace the idealized hypoxia conditions with realistic DO concentrations generated from a 3-dimensional water quality model. Three years were used and randomly arranged into a time series based on the historical occurrence of mild, intermediate, and severe hypoxia year types.We also used another water quality model to generate multipliers of the chlorophyll concentrations to reflect that croaker food can be correlated to the severity of hypoxia. Simulations used 100 years under normoxia and hypoxia conditions to examine croaker population responses to the following: (1) hypoxia with food uncoupled and coupled to the severity of hypoxia, (2) hypoxia reducing benthos due to direct mortality, (3) how much hypoxia would need to be reduced to offset decreased croaker food expected under 25 and 50% reduction in nutrient loadings, and (4) key assumptions about avoidance movement. Direct mortality on benthos had no effect on long-term simulated croaker abundance, and the effect of hypoxia (about a 25% reduction in abundance) was consistent whether chlorophyll (food) varied with hypoxia or not. Reductions in hypoxia needed with a 25% reduction in nutrient loadings to result in minimal loss of croaker is feasible, and the croaker population will likely do as well as possible (approach abundance under normoxia) under the 50% reduction in nutrient loadings. We conclude with a discussion of why we consider our simulation-based estimates of hypoxia causing a 25% reduction the long-term population abundance of croaker in the NWGOM to be realistic and robust

Improved Efficiency and Sensitivity Analysis of 3-D Agent-based Model for Pain-related Neural Activity in the Amygdala

This OSF site contains the NetLogo3D code and supporting files for the computational model presented in the SPORA article titled 'Improved Efficiency and Sensitivity Analysis of 3-D Agent-based Model for Pain-related Neural Activity in the Amygdala'

Figure 5

This component contains the data and R code used to create Figure 5

Table 1

This component contains Table 1

Agent-based modeling of the central amygdala and pain using cell-type specific physiological parameters (NetLogo code and data files)

NetLogo code and related files for simulation of a 2-D agent-based model of pain-related neurons in the central amygdal

Figure 1

This component contains the data and R code used to create Figure 1

Table 2

This component contains Table 2