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7.4.1. What diseases other than gonorrhea might be modeled with the two- population S/S model developed here? 7.4.2. A certain sexually transmitted disease is described by the model of this section. Suppose for a female population of 10,000 and a male population of 15,000, the transmission coefficients are a = .0000009 and a" = .000006, and the removal rates are y/ = .007 and y" = 05. a. Are females more likely to catch the disease than males? Which sex is likely to recover more quickly? b. Find the maximal female contact number and the maximal male contact number. Do you expect the disease to be endemic? Check your result with a computer simulation. c. Calculate NAN" - p/p". Then, use this expression to solve for the equilibrium values of S/, If, S", /" . Use a computer program such as twopop to verify your solutions.d. Run a computer program such as twopop to determine if the nonzero equilibria are stable or unstable. Use a variety of choices for your initial infective populations. 7.4.3. Suppose when modeling a heterosexually transmitted disease, you find that a = .011, a" = .00023, y= .5, and y" = .2. a. If the time step is 1 day, what are the characteristics of this disease? Include a discussion of the meaning of the transmission coefficients and removal rates for each sex. b. Suppose the population is fixed with 500 people, 100 females and 400 males. Calculate the maximal female and male contact numbers. Can the disease be endemic? Explain. What if instead there are 50 females and 450 males, or if the population is evenly divided, 250 females and 250 males? 7.4.4. An infectious disease hits an isolated community. The elderly pop- ulation is especially vulnerable; they catch the disease more readily and are slower to recover than are the young. Suppose you attempt to describe this using a two-population S/S model of the form: AS = -a'S, (1, + 1," ) +yell. AS' = -a"S, (1; + 1/ ) +y'll. a. Assuming there are a total of A elderly people and Ny young people, rewrite the model to eliminate / and I. b. If the a values are .0003 and .0001, which is a and which is a "? If the y values are .21 and .05, which is y and which is y"? c. Use a computer program such as twopop to determine what hap- pens to the two populations using the parameter values in part (b), along with N = 250 and Ny = 750. 7.4.5. The text claims that the nonzero equilibrium solution for the two- population SIS model of gonorrhea occurs when 1/ = NIN"-p/pm p/+Nm and /m = NIN"-PP" Verify this as follows: a. Using A/ / = 0, show that at equilibrium NSIm Give a similar formula for /" at equilibrium