Elsa Schaefer

Modeling optimal intervention strategies for cholera.

While cholera has been a recognized disease for two centuries, there is no strategy for its effective control. We formulate a mathematical model to include essential components such as a hyperinfectious, short-lived bacterial state, a separate class for mild human infections, and waning disease immunity. A new result quantifies contributions to the basic reproductive number from multiple infectious classes. Using optimal control theory, parameter sensitivity analysis, and numerical simulations, a cost-effective balance of multiple intervention methods is compared for two endemic populations. Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods.

Metapopulation Models in Tick-Borne Disease Transmission Modelling

Human monocytic ehrlichiosis (Ehrlichia chaffeensis), or HME, is a tick-transmitted, ricksettisal disease with growing impact in the United States. Risk of a tick-borne disease such as HME to humans can be estimated using the prevalence of that disease in the tick population. A deterministic model for HME is explored to investigate the underlying dynamics of prevalence in tick populations, particularly when spatial considerations are allowed. The dynamics of HME in a single spatial patch are considered first to determine which model components are most important to predicting disease dynamics in a local ecology. The model is then expanded to spatially-explicit patches on which patch connectivity, the surrounding environment and boundary effects are studied. The results of this investigation show that predicting risk of this disease to humans is determined by many complicated interactions. Areas that would be endemic in isolation may or may not sustain the disease depending on the surrounding habitat. Similarly, control efforts are shown to be far more effective when applied in wooded habitats than in neighboring grassy habitats. Boundary assumptions which describe the reality of increasing habitat fragmentation additionally play a large role in predicting the endemicity of an HME outbreak. Overall, HME and all tick-borne diseases are complex, nonlinear systems that have just begun to be explored.

An evolutionary computing approach for parameter estimation investigation of a model for cholera

We consider the problem of using time-series data to inform a corresponding deterministic model and introduce the concept of genetic algorithms (GA) as a tool for parameter estimation, providing instructions for an implementation of the method that does not require access to special toolboxes or software. We give as an example a model for cholera, a disease for which there is much mechanistic uncertainty in the literature. We use GA to find parameter sets using available time-series data from the introduction of cholera in Haiti and we discuss the value of comparing multiple parameter sets with similar performances in describing the data.

Results from a mathematical model for human monocytic ehrlichiosis.

Human monocytic ehrlichiosis (Ehrlichia chaffeensis), HME, is a tick-transmitted, rickettsial disease that has recently increased substantially in the USA from 142 reported cases in 2001 to 506 reported cases in 2005 [1,2]. There have been increasing surveys of tick populations over the past 10 years that have in turn supported the development of models for tick-borne disease transmission. Resulting HME models [3] suggest the importance of metapopulation structures, landscape environment parameters and periodic climatic effects in predicting the dynamics of HME transmission and the efficacy of control efforts, such as the reduction of the tick population through acaricide use. On this note, we describe a spatially-explicit model for HME

Use of optimal control models to predict treatment time for managing tick-borne disease

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 ticks life history plays a critical role in reducing risk without the need for a permanent treatment programme. This work suggests that across a variety of optimal control frameworks and objective functionals within a closed environment, similar strategies are created, all suggesting that the tick-borne disease risk can be reduced to near zero without completely eliminating the tick population.

Examination of models for cholera: insights into model comparison methods

This article provides an overview of the Akaike and Bayesian Information Criteria as applied to the setting of deterministic modelling, with the perspective that this may be a useful tool for biomathematics researchers whose primary interests lie in the analysis of compartmental models. We additionally examine a wide range mechanistic and parameter assumptions in the cholera literature through the unifying lens of model selection criteria. Five models for cholera are considered using multiple model selection formulations, and implications for cholera modelling and for model selection criteria are discussed.

Optimal Control of Vaccination in an Age-Structured Cholera Model

A cholera model with continuous age structure is given as a system of hyperbolic (first-order) partial differential equations (PDEs) in combination with ordinary differential equations. Asymptomatic infected and susceptibles with partial immunity are included in this epidemiology model with vaccination rate as a control; minimizing the symptomatic infecteds while minimizing the cost of the vaccinations represents the goal. With the method of characteristics and a fixed point argument, the existence of a solution to our nonlinear state system is achieved. The representation and existence of a unique optimal control are derived. The steps to justify the optimal control results for such a system with first order PDEs are given. Numerical results illustrate the effect of age structure on optimal vaccination rates.

Parameter Estimation in Ordinary Differential Equations Modeling via Particle Swarm Optimization

Researchers using ordinary differential equations to model phenomena face two main challenges among others: implementing the appropriate model and optimizing the parameters of the selected model. The latter often proves difficult or computationally expensive. Here, we implement Particle Swarm Optimization, which draws inspiration from the optimizing behavior of insect swarms in nature, as it is a simple and efficient method for fitting models to data. We demonstrate its efficacy by showing that it outstrips evolutionary computing methods previously used to analyze an epidemic model.