According to the SI model of disease discussed in class, the number of individuals I infected...

 

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According to the SI model of disease discussed in class, the number of individuals I infected by a disease changes in time t according to the logistic equation dI = rI (1-7), dt where r > 0 is the initial growth rate of the infected population and N> 0 is the total population (assumed to be constant, i.e., no dying). The number of individuals susceptible to the disease S can be determined according to S = N - I. a. Assume the initial infected population is Io. Determine a formula for the infected population as a function of time t. b. Suppose Io<N/2. At what time is the infected population equal to the susceptible population? Does this time increase or decrease if we... increase the initial growth rate of disease r? • increase the population size N? increase the initial number of infected individuals Io? c. According to the SI model, is anyone safe from disease or are we all doomed? Use your answer from (a) to justify your answer. Remark: This is one of the reasons why the SI model is incomplete/unphysical. According to the SI model of disease discussed in class, the number of individuals I infected by a disease changes in time t according to the logistic equation dI = rI (1-7), dt where r > 0 is the initial growth rate of the infected population and N> 0 is the total population (assumed to be constant, i.e., no dying). The number of individuals susceptible to the disease S can be determined according to S = N - I. a. Assume the initial infected population is Io. Determine a formula for the infected population as a function of time t. b. Suppose Io<N/2. At what time is the infected population equal to the susceptible population? Does this time increase or decrease if we... increase the initial growth rate of disease r? • increase the population size N? increase the initial number of infected individuals Io? c. According to the SI model, is anyone safe from disease or are we all doomed? Use your answer from (a) to justify your answer. Remark: This is one of the reasons why the SI model is incomplete/unphysical.