Applied Mathematics Commons^™

Impact Of Vaccine Supplies And Delays On Optimal Control Of The Covid-19 Pandemic: Mapping Interventions For The Philippines, Carlo Delfin S. Estadilla, Joshua Uyheng, Elvira P. De Lara-Tuprio, Timothy Robin Y. Teng, Jay Michael R. Macalalag, Ma. Regina Justina E. Estuar

Mathematics Faculty Publications

Background

Around the world, controlling the COVID-19 pandemic requires national coordination of multiple intervention strategies. As vaccinations are globally introduced into the repertoire of available interventions, it is important to consider how changes in the local supply of vaccines, including delays in administration, may be addressed through existing policy levers. This study aims to identify the optimal level of interventions for COVID-19 from 2021 to 2022 in the Philippines, which as a developing country is particularly vulnerable to shifting assumptions around vaccine availability. Furthermore, we explore optimal strategies in scenarios featuring delays in vaccine administration, expansions of vaccine supply, and …

Population Modeling For Resource Allocation And Antimicrobial Stewardship, Jason Bintz

Doctoral Dissertations

This dissertation contains two types of population models with applications in conservation biology and epidemiology. In particular, it considers models for resource allocation and antimicrobial stewardship.

In a population model with a parabolic differential equation and density dependent growth, we study the problem of allocating resources to maximize the net benefit in the conservation of a single species while the cost of the resource allocation is minimized. The net benefit is measured in terms of maximizing population abundance and the goal of maximizing abundance is divided between the goal of maximizing the overall abundance across space and time and the …

Use Of Optimal Control Models To Predict Treatment Time For Managing Tick-Borne Disease, Holly D. Gaff, Elsa Schaefer, Suzanne Lenhart

Biological Sciences Faculty Publications

Tick-borne diseases have been on the rise recently, and correspondingly, there is an increased interest in implementing control measures to decrease the risk. Optimal control provides an ideal tool to identify the best method for reducing risk while accounting for the associated costs. Using a previously published model, a variety of frameworks are assessed to identify the key factors influencing mitigation strategies. The level and duration of tick-reducing efforts are key metrics for understanding the successful reduction in tick-borne disease incidence. The results show that the punctuated nature of the tick's life history plays a critical role in reducing risk …

Optimal Therapy Regimens For Treatment-Resistant Mutations Of Hiv, Weiqing Gu, Helen Moore

All HMC Faculty Publications and Research

In this paper, we use control theory to determine optimal treatment regimens for HIV patients, taking into account treatment-resistant mutations of the virus. We perform optimal control analysis on a model developed previously for the dynamics of HIV with strains of various resistance to treatment (Moore and Gu, 2005). This model incorporates three types of resistance to treatments: strains that are not responsive to protease inhibitors, strains not responsive to reverse transcriptase inhibitors, and strains not responsive to either of these treatments. We solve for the optimal treatment regimens analytically and numerically. We find parameter regimes for which optimal dosing …