BME210 Spread_of_Disease - Copy

BME210 Spread_of_Disease - Copy - BME 210 Spring 2009...

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BME 210 Spring 2009 Modeling the Spread of Disease BME 210 Biomedical Computer Simulation Methods Modeling Spread of Disease I Introduction to the Spread of Disease II. Computer Simulation of Chance Events III. One Population Spread of Disease Problem Defined IV. Simulating the One Population Spread of Disease Problem Study Problems Study Problem Solutions
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BME 210 Spring 2009 Modeling the Spread of Disease 2 Modeling the Spread of Disease I. Introduction to the Spread of Disease In this section, we will be concerned with some aspects of the study of the spread of disease (i.e., epidemiology). While much of the field of epidemiology deals with analysis of data resulting from studies on the incidence and spread of disease in a population, we will be concerned here with some simple mathematical models for predicting patterns in the spread of disease. To do this we must consider how we can use the computer to simulate the random or chance events, which are fundamental to the spread of disease process. Let us first, however, introduce some general ideas and concepts regarding the propagation of disease in a population. To do this, consider the following figure which divides a population into four subpopulations depending on whether a subject has or has had a specific disease. Healthy Infected Contagious → . . Healthy not immune incubation period recuperation period immunity period From left to right, we have the following progress of disease. A healthy subject can contract the disease if he or she has no immunity to it and comes in contact with a person who is contagious, in which case the subject becomes infected . The duration of time in which the subject is infected is termed the incubation period, the extent of which can differ somewhat from one subject to the next. In the next stage of the spread of a disease the infected subject becomes contagious, during which time the disease can be transmitted to another healthy non-immune subject. The duration of time the subject remains contagious is referred to as the recuperation period. Finally, the subject will become healthy again but with an acquired immunity , the duration of which depends on the disease. II. Computer Simulation of Chance Events Certain types of physical systems and the models associated with these systems are said to be deterministic . For such systems, the characteristics of the models (its parameters) and the selected inputs completely determine the outputs. For instance, when the resistance of air is neglected, the movement of a ball is completely determined by its mass, its initial velocity, and the gravitational constant. The processes associated with the spread of disease, on the other hand, are said to be stochastic , because the results of the process are subject to uncertain and random events. The tools we need to simulate these stochastic processes are quite different from those we need to solve the equations representing deterministic systems. The class of techniques developed for computer simulation of random or chance events are referred to as Monte Carlo methods.
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This note was uploaded on 09/09/2010 for the course BME 210 taught by Professor D'argenio during the Spring '07 term at USC.

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BME210 Spread_of_Disease - Copy - BME 210 Spring 2009...

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