ogunmiloro

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5 years, 148 days

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These are replies submitted by ogunmiloro

@mmcdara thanks for your response. Absence of infection I mean disease free equilibrium solution. Va(t) is the only susceptible state. That Q is a mistake I intend to write Big \Phi . The remaining state equations are infectious. Thanks 

@rcorless Thanks very much. The t versus T is a typo. It should read t. The eigenvalues or polynomila generated is so cumbersome. Please correct type t versus T and do the remaining computation. Thanks

@mmcdara 

The values F[d] = 1.00, L[d] = 2. 018, E_c = 1.10 while the initial condition G_[dp] = 1. 023

@mmcdara

Thanks for your response. I need to answer your question one after ther other

(1) For each year the GDP amount in Naira (Name of the currency) is specified. For instance, for the year 2022, the GDP generated is over 3 million naira (year 2022 = 3, 023, 744. 14 naira). This goes for the remaining year too. 

(2) The data represents the gross domestic (in millions) generated from education in a country from year 2015 - 2022

(3) I intend to solve the ode, where diff(G[dp](T), T) is a compartmental variable and psi[i](i=1-3) and delta[3] denotes the different contribution rates and loss of G[dp] respectively

(4) the parameters are the inital parameters, but i intend to generate another set of parameter values through some minimization methods
and F[d], L[d] and E[c] are functions of time

@Rouben Rostamian

(1)As you said that the first three eigenvalues are large, cant maple or a code be made to simplify the size of the Large eigen values?

Or alternatively construct a quadratic polynomial to express it

@tomleslie the data is real. The observations are recorded weekly for 52 weeks. It's only the fitting function that I think I have problem with

@mmcdara 
 

restart

with(LinearAlgebra); A := Matrix(5, 5, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = tau*`Πu`/mu, (3, 4) = 0, (3, 5) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = `ϖ`*`Πg`/mu}); B := Matrix(5, 5, {(1, 1) = mu, (1, 2) = 0, (1, 3) = 0, (1, 4) = gamma, (1, 5) = 0, (2, 1) = 0, (2, 2) = mu+omega, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = mu+sigma1, (3, 4) = theta, (3, 5) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = alpha2+gamma+mu, (4, 5) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = sigma1+alpha2, (5, 4) = 0, (5, 5) = theta}); C := A.(1/B); Rank(C); evs := Eigenvalues(C); eig := op(`minus`({entries(evs, nolist)}, {0}))

A := Matrix(5, 5, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = tau*`Πu`/mu, (3, 4) = 0, (3, 5) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = `ϖ`*`Πg`/mu})

 

B := Matrix(5, 5, {(1, 1) = mu, (1, 2) = 0, (1, 3) = 0, (1, 4) = gamma, (1, 5) = 0, (2, 1) = 0, (2, 2) = mu+omega, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = mu+sigma1, (3, 4) = theta, (3, 5) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = alpha2+gamma+mu, (4, 5) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = sigma1+alpha2, (5, 4) = 0, (5, 5) = theta})

 

C := Matrix(5, 5, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = tau*`Πu`/(mu*(mu+sigma1)), (3, 4) = -tau*`Πu`*theta/(mu*(alpha2+gamma+mu)*(mu+sigma1)), (3, 5) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = -`ϖ`*`Πg`*(sigma1+alpha2)/(mu*(mu+sigma1)*theta), (5, 4) = `ϖ`*`Πg`*(sigma1+alpha2)/(mu*(alpha2+gamma+mu)*(mu+sigma1)), (5, 5) = `ϖ`*`Πg`/(mu*theta)})

 

2

 

evs := Vector(5, {(1) = 0, (2) = 0, (3) = 0, (4) = tau*`Πu`/(mu*(mu+sigma1)), (5) = `ϖ`*`Πg`/(mu*theta)})

 

`ϖ`*`Πg`/(mu*theta), tau*`Πu`/(mu*(mu+sigma1))

(1)

params := {`Πg` = 2.2, `Πu` = 3.4, `ϖ` = 0.96e-1, alpha2 = .33, mu = .2041, omega = .5, sigma1 = .72, tau = .33, theta = .9};

{`Πg` = 2.2, `Πu` = 3.4, `ϖ` = 0.96e-1, alpha2 = .33, mu = .2041, omega = .5, sigma1 = .72, tau = .33, theta = .9}

(2)

``

# what are you trying to plot?

eval(eig, remove(has, params, varpi));

1.149763188, 5.948820737

(3)

# two ways :
#  1/ plot these 2 quantities

plot([eval(eig, remove(has, params, varpi))], varpi = 0 .. .5, filled = true, thickness = 4, color = [blue, red], transparency = .4);

 


#  2/ plot only the last one

plot(eval(eig, remove(has, params, varpi))[2], varpi = 0 .. .5, filled = true, thickness = 4, color = blue, transparency = .4);

 

 


 

Download graph_mmcdara.mw Issues
(1) After running the code the behavior of the graph i observed is not the same as the one you plotted (using the same variable values). What could be the reason?
(ii) Pig means (One of the variables in Params Pig against varpi), that is, plotting two variables (in Params) against each other. Thanks

@mmcdara thanks for your effort. Please can you plot Pig against sigma1 (I mean two parameters against each other and not against eig)

@acer Thank you very much for the job well done

@mmcdara I thank you very much for the job well done

@mmcdara Oh I'm very sorry. Your contribution have been very useful to me and the scientific community. I'm gonna get the new version soonest to handle the graphs. ***my question really is how to obtain the stationary points of the new matrixPP since the method you earlier use cannot handle that. Thanks

@mmcdara 
Thanks so far. I have re-evaluated the transtion martrix (PP). The graph obtained is given.
(1)The stationary values are to be obtained since the former method for 2 states cannot work for this
(2) The long term analysis and other statistical analysis are needed to be performed
The work sheet is attached below the graph


re-markov.mw

@mmcdara 
Thanks for your good effort so far. Questions
(1) Since the problem reduces to a two state problem. How can one predict/simulation which of the states will likely prevail or extinct?
(2) You proposed a method for the two state problem, what is the name of the analytical method?
 

@mmcdara Thank you very much for the effort.

@itsme thanks very much

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