The Kermack-McKendrick equations are first order differential equations describing an infectious disease outbreak. Using S to denote the number of susceptible members of the population and I to denote the number of infected members, the equations are S'= - BSI I = BSI – EI, where ß and μ are positive constants representing the transmission rate and rate of recovery. Construct the phase plane, including all nullclines, equilibria, and arrows indicating the direction of movement in the plane.

Q: brick weighting 27lbs is thrown downward at a of 2 ft/sec and has a wind resistance that is 3% of…

A: (a) Given that v=2 ft/sec, and wind resistance is 0.03v2 And m=27 lbs g=32 ft/sec2 Using ma=mq-kv2…

Q: Rewrite the following 3rd order differential equation as a first order system of equations. u" + 7u"…

A: The given 3rd order differential equation is                       u'''+7u''+5u'+10u=5

Q: For each differential equation, indicate the order (as a number) and whether the equation is linear…

A:

Q: The roots of an auxiliary cubic equation are m1=-1 and m2=m3=-5. What is the corresponding…

A: We have given the roots of an auxiliary cubic equation ,  m1 = -1  , m2 = m3 = -5 Thus , Auxiliary…

Q: (e) If an initial condition of x(0) = 1, sketch the x(t) vs t graph. (f) Use the Euler method to…

A: We have to sketch the graph of the differential equation