# A certain type of bacteria has been incubating within infect

A certain type of bacteria has been incubating within infected tissues. Let P(t) denote the bacteâ€¦ Show more A certain type of bacteria has been incubating within infected tissues. Let P(t) denote the bacteria population, P>or equal to 0, as a function of time(measured in hours), per unit volume of tissues. Let t=0 to be the time that the patientâ€™s immune system begins responding to the antigens. Suppose the bacteriaâ€™s growth is continuous with a rate of growth equals twice of its present polulation size, and that the patientâ€™s immune system is able to reduce P by 9000, per hour. THe progress of the infection can be modeled by the first order differential equation for (t>0): Pâ€™=2P-9000 (a) Does the equation have an equilibrium solution? If it does, find it and classify its stability. (b) Suppose P(0)=6000, per hour. what is the patientâ€™s prognosis? (c)Proper vaccination would provide the host with a stockpile of antibodies keyed to the specific antigens, thereby speeds up the immune systemâ€™s response time. The immune system would, therefore, responds while P(t) is at a lower count than otherwise. Suppose the immune system of an infected, but vaccinated, patient responds at P(0)=3000, what is this patientâ€™s prognosis? (d) A proplerly applied antibiotics regimen will increase the rate of reduction of P to 15000per hour. Under such treatment, the equation describing P becomes Pâ€™=2P-15000. Once again, suppose P(0) = 6000, what is the patientâ€™s prognosis? â€¢ Show less

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