Leptospirosis models: vaccination of cattle and early detection in humans

In this dissertation we discuss two mathematical models for leptospirosis. The first project is a mathematical model of leptospirosis with impulse actions in cattle. The project is to understand the propagation of leptospirosis and find a schedule for control programs to eradicate the disease in a cattle ranch. An epidemiological model has been built with ordinary differential equations (ODEs) and included some vaccination and recruitment control programs in the form of impulse actions to prevent the propagation of leptospirosis in the ranch. This system of ODEs with impulse actions determines a schedule of control actions in order to eradicate leptospirosis in the ranch. Parameter estimation and sensitivity analysis were completed as a part of this study. The second project is a stochastic optimization model for cost effectiveness analysis in early detection of leptospirosis in humans. To seek an optimal treatment strategy for the patients coming into a hospital with the symptoms similar to those of leptospirosis, a stochastic processing model with a computational algorithm was developed to compare treatment strategies and determine an optimal management strategy maximizing the number of early detected leptospirosis cases and minimizing the corresponding costs.