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.

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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Question

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.

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