hw5solutions_BME210_2007 - BME210 Spring2007 BME 210...

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BME210 Spring2007 BME 210 Homework 5 Solutions Modeling the Spread of Disease Introduction: The field of epidemiology is the study of the causes, distribution, and control of disease in populations. This homework combines ideas from this branch of medicine with engineering concepts in order to model the spread of disease in a single population. The problem of predicting this has been developed in H. G. Wells’s The War of the Worlds, in which the demise of the martial population was developed. The spread of disease follows this progression: Healthy Infected Contagious Healthy (Non Immune) (Incubation) (Recuperation) (Immune) From left to right, we have the following progress if disease. A healthy subject can contract the disease if he 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. In order to implement these types of populations into a computer language, we make several assumptions and definitions. The array M, with N (number of individuals) elements, tells us the state of healthy of each individual and has the following designations: M(i)=0 means the ith persons is healthy; M(i)<0 means the ith person is infected, and M(i)>0 means the ith person is contagious. Then the array IM indicates the immunity status of each subject, IM(i) 0 means the ith person is not immune, while IM(i)<0 means the ith person is immune. These two arrays, M and IM, indicate if the subject is healthy, infected, or contagious, and if the subject is healthy, his immune status. The basic outline for the program, to simulate the spread of disease is as follows: 1. Initialize subpopulations -select the specific individuals to be assigned to each subpopulation 2. Sample Period Loop a. Randomly expose population b. Record and store NI, NC, NHI, and NH c. Update M(i) and IM(i) 3. Next sample period (go to Step 2) or end loop 4. Output results
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