The transmission dynamics of a disease in a population is represented by the equation ما بين ,al - ( - 1) - معمل انتقال العرض عمل الأنتقال -Cal dt BI K - اسگان where I is the number of infected individuals in the population, ß denotes the transmission coefficient, K is the total population size and a the recovery rate. Assume that K>0, a>0 and 3>0. 2 (a) Find the steady-state solutions of this model and determine their stability as a function of the: rate a). I represent eradication recovery endawie (b) Hence, or otherwise, determine the condition for the disease to be eradicated. I represets (c) Draw a steady-state diagram for this model treating the recovery rate, a, as the control parameter. Indicate stable and unstable steady-state solutions using solid and dashed lines respectively. due
The transmission dynamics of a disease in a population is represented by the equation ما بين ,al - ( - 1) - معمل انتقال العرض عمل الأنتقال -Cal dt BI K - اسگان where I is the number of infected individuals in the population, ß denotes the transmission coefficient, K is the total population size and a the recovery rate. Assume that K>0, a>0 and 3>0. 2 (a) Find the steady-state solutions of this model and determine their stability as a function of the: rate a). I represent eradication recovery endawie (b) Hence, or otherwise, determine the condition for the disease to be eradicated. I represets (c) Draw a steady-state diagram for this model treating the recovery rate, a, as the control parameter. Indicate stable and unstable steady-state solutions using solid and dashed lines respectively. due
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3. The transmission dynamics of a disease in a population is represented by the equation
-(²-1 (1-1)-0
معدل انتقال المرضى
ة من الانتقال
al,
عدد السكان
where I is the number of infected individuals in the population, ß denotes the transmission coefficient, K
is the total population size and a the recovery rate. Assume that K>0, a > 0 and > 0.
(a) Find the steady-state solutions of this model and determine their stability as a function of the recovery
rate a).
I: represente eradication of the
(b) Hence, or otherwise, determine the condition for the disease to be eradicated. I: repisal: an andanic discuse.
(c) Draw a steady-state diagram for this model treating the recovery rate, a, as the control parameter.
Indicate stable and unstable steady-state solutions using solid and dashed lines respectively.
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