The simplest model of malaria assumes that the mosquito population is at equi- librium and models the proportion of the infected humans I with the following equa- tion: aßI :(1-1) - ul, al +r where r is the natural death rate of mosquitoes, u is the death rate of humans, B is the transmission rate from infected mosquitoes to susceptible humans, and a is the transmission rate from humans to mosquitoes.

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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Given that alpha, beta, r and mu > 0. 

a) Find parameters for alpha, beta, r and mu so that the disease dies out. 

b) Using a phase line, we see that the model has a positive equilibrium. What is that equilibrium?

The simplest model of malaria assumes that the mosquito population is at equi-
librium and models the proportion of the infected humans I with the following equa-
tion:
aBI
:(1– 1) – µl,
where r is the natural death rate of mosquitoes, u is the death rate of humans, B is
the transmission rate from infected mosquitoes to susceptible humans, and a is the
transmission rate from humans to mosquitoes.
Transcribed Image Text:The simplest model of malaria assumes that the mosquito population is at equi- librium and models the proportion of the infected humans I with the following equa- tion: aBI :(1– 1) – µl, where r is the natural death rate of mosquitoes, u is the death rate of humans, B is the transmission rate from infected mosquitoes to susceptible humans, and a is the transmission rate from humans to mosquitoes.
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