Hem Raj Joshi

Optimal harvesting during an invasion of a sublethal plant pathogen

Plant pathogens are quite destructive to cash crops throughout the world, resulting in potentially devastating financial losses. This work expands recently developed optimal control theory for an integrodifference model to a mathematical system which includes an integrodifference component. This system models a highly simplified plant pathogen system for which the optimal harvesting scheme is derived. An adjoint system is introduced to characterize the optimal harvesting pattern. This analysis shows that, while it may not be possible to prevent losses upon discovery of the pathogen in an area, it is theoretically possible to significantly cut those losses by culling an area around the initial infection.

Economic Recession and Headache-Related Hospital Admissions

Abstract Incidence of headaches across different regions and its relationship to unemployment rates in the United States before and during an economic recession was evaluated. Years 2008 and 2009 were determined as recessionary period. Headache-related admissions, particularly the uncomplicated headaches, increased significantly during recession. Proportion of women with headaches has increased and the age group of 25–54 years was the most affected during the recession. The hospital charges have increased even though the average length and charge of stay decreased. These findings are consistent with our understanding of effects of stress and unemployment on psychological and physical health.

Illustrating Optimal Control Applications with Discrete and Continuous Features

In this paper, we present the basic idea of optimal control of models with discrete and continuous features. We first consider ordinary differential equation (ODE) models where we emphasize problems which are linear in the control and have discrete values for the optimal control. Three examples with ODEs illustrate how the bang-bang and singular controls could be handled. The first example utilizes a simple model with one ODE. The next two examples use systems of ODEs. One example comes from a mobile robot with one or more steerable drive wheels that steer together. The other example models species augmentation where two populations of the same species are modeled with a target/endangered population and a reserve population. Then we present an extension to an integrodifference model that is discrete in time and continuous in space. This optimal pest control problem is modeled by integrodifference equations and we illustrate how to construct the necessary conditions.