# What is the patients prognosis?

A certain type of bacteria has been incubating within infected tissues. Let P(t) denote the bacteria Show more A certain type of bacteria has been incubating within infected tissues. Let P(t) denote the bacteria population P >=0 as a function of time (measured in hours) per unit volume of tissue. Let t=0 be the time that the patients immune system begins responding to the antigens. Suppose the bacterias growth is continuous with the rate of growth equals twice of its present population size and that the patients immune system is able to reduce p by 8000 per hour. the progress of the infection can be modeled by the first-order differential equation (for t >0): (a) Find its general solution. Does the equation have an equalibrium solution? If it does find it and classify its stability (b) Suppose P(0) = 5000 Whats is the patients prognosis? (c) Proper vaccination would provide the host with stockpile of antibodies keyed to the specific antigens thereby speeds up the immune system response time. The immune system would therefore responds while P(t) is at a lower count than otherwise. Suppose the immune system of an infeced but vaccinated patient responds at P(0)= 3000 What is the patients prognosis? (d) A properly applied antibiotics regimen will increase the rate of reduction of P to 12000 per hour. Under such treatment the equation describing P becomes Again suppose P(0)=5000. What is the patients prognosis? Show less