To reduce the model which is a third order system to a first-order system that can be analyzed by our methods The equations are x . = - kxy y . = kxy - ly z . = ly Concept Introduction: Epidemic model which describes the transmission of communicable diseases through individuals. People get sick at the rate proportional to product of x and y. Healthy and sick people encounter to each other at rate proportional to their numbers. Sick people die at a constant rate l. The given equations are based on the above two assumptions.

Question

Want to see the full answer?

Answer 1

Question

Chapter 3.7, Problem 6E

Interpretation Introduction

Interpretation:

To reduce the model which is a third order system to a first-order system that can be analyzed by our methods

The equations are

x. = - kxy

y. = kxy - ly

z. = ly

Concept Introduction:

Epidemic model which describes the transmission of communicable diseases through individuals.

People get sick at the rate proportional to product of x and y. Healthy and sick people encounter to each other at rate proportional to their numbers.

Sick people die at a constant rate l.

The given equations are based on the above two assumptions.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

Find the first four nonzero terms in a power series expansion about x=0 for a general solution to the given differential equation w''-14x^2w'+w=0

In this exercise, we will investigate a technique to prove that a language is notregular. This tool is called the pumping lemma.The pumping lemma says that if M = (S, I, f, s0, F ) is a DFA with p states (i.e., p = |S|) and if the wordw is in L(M ) (the language generated by M ) and w has length greater than or equal to p, then w may bedivided into three pieces, w = xyz, satisfying the following conditions:1. For each i ∈ N, xy^i z ∈ L(M ).2. |y| > 0 (i.e., y contains at least one character).3. |xy| ≤ p (i.e., the string xy has at most p characters). Use the pumping lemma to show the following language is not regular (HINT: Use proof by contradictionto assume the language is regular and apply the pumping lemma to the language):L = {0^k1^k | k ∈ N}

A prefix of length ℓ of some word w are the first ℓ characters (in order) of w.1. Construct a context-free grammar for the language: L = {w ∈ {a, b}∗ | every prefix of w has at least as many a’s as b’s}2. Explain why every word generated by your context-free grammar (in Part 1) is contained in L. Then,prove via induction that every w ∈ L is produced by your context-free grammar.