STABILITY ANALYSIS AND OPTIMAL VACCINATION OF A WATERBORNE DISEASE MODEL WITH MULTIPLE WATER SOURCES

Waterborne diseases are among the major health problems facing the world today. This is especially true in developing countries where there is limited access to clean water. In such settings, even when multiple water sources exist, they tend to be contaminated. In this paper, we formulate a waterborne disease model where individuals are exposed to multiple contaminated water sources. The fundamental mathematical features of the model such as the basic reproduction number and final epidemic size are obtained and analyzed accordingly. The global stability analysis of the disease‐free equilibrium is performed. The model is later extended by considering vaccination as a possible control intervention strategy. An optimal control problem is constructed to investigate the existence of an optimal control function that reduces the spread of the disease with minimum cost. We support our analytical predictions by carrying out numerical simulations using published and estimated data from the recent cholera outbreak in Haiti.     

Controllability and Canonical Forms for Multipass Systems Described by Linear Ordinary Differential Equations

The controllability and reachability of multipass systems governedby linear ordinary differential equations are considered andsome results given on canonical forms for such systems. Theseresults are used to construct deadbeat controllers.     

The Solution of a Statistical Decision Problem with Moving Boundaries by the Image Method

Temporary address: Department of Theoretical Physics, University of Manchester. A point executes Brownian motion in one dimension, startingfrom a known initial position. Its velocity at any time is asuperposition of a constant "drift" speed and a random, diffusivecomponent, the motion taking place between two absorbing boundarieswhich move towards one another with constant speeds. The probabilitydistribution for the particle position at any time is foundby the method of images. The problem occurred originally inthe detection of a small d.c. signal in a large amount of "white"noise, and this application is discussed.