Taken from \" Thermodynamics- Statistical Thermodynamics and Kinetics\" by Thoma

Question

Taken from " Thermodynamics- Statistical Thermodynamics and Kinetics" by Thomas Engel and Philip Reid

The Kermack-McKendrick model was developed to explain the rapid rise and fall in the number of infected people during epidemics. This model involves the interaction of susceptible (S), infected (I), and recovered (R) people through the following mechanism: Write down the differential rate expressions for S, I, and R. The key quantity in this mechanism is called the epidemiological threshold defined as the ratio of [S]k_1/k_2. When this ratio is greater than 1 the epidemic will spread; however, when the threshold is less than 1 the epidemic will die out. Based on the mechanism, explain why this behavior is observed.

Explanation / Answer

I am only answering the part b) as requested in comments

This particular model called the Kermack-McKendrick Model is a model for the number of people infected with a contagious illness in a closed population over time.

The key value governing the time evolution of these equations is the so-called epidemiological threshold,

R = [S] x k1/k2

When R<1, each person who contracts the disease will infect fewer than one person before dying or recovering, so the outbreak will die out.

As you can see from the equation if R is a fraction(since it is less than 1). The terms k1/k2 should be a very small number since [S] will be the entire population and is large.

Now k1/k2 will be small when the rate at which number of people are being infected is much smaller than the rate at which people are recovering.

So the disease is dying out.

When R>1, each person who gets the disease will infect more than one person, so the epidemic will spread.

As you can see from the equation if R is a greater than 1. The terms k1/k2 will be a whole number.

Now k1/k2 will be large when the rate at which number of who are being infected is much larger than the rate at which people are recovering.

So the disease is spread more.

Hope this explains the question

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.