University of California Merced Modeling Pandemic Infection Rates Worksheet
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This is a questions for a differential equations course. Please show all steps (for example, if you need to integrate by parts show all parts).
The problem is worded like the one below:
We are modeling pandemic infection rates. X represents vulnerable people and y is the proportion of carriers in the population. Carriers can be removed from population at rate B, so dy/dt = -By. Disease spreads at a rate in proportion to x and y: dx/dt = -axy. Please solve for y (using first equation) at any time t assuming initial condition y(0)=y1 and use this to solve for x (using the second equation) assuming initial condition x(0)=x1. What proportion of the population avoids the pandemic?
