@sazroberson 

Yep, I do use Sample() to get particular values.

Thanks for the tip anyway,

jon

@Carl Love 

Sorry Carl. You are right.

The second worksheet is this: MaplePrimes_SIR_model_simulation_Gillespie_algorithm_proc.mw

Thanks,

jon

@Preben Alsholm

Dear Preben Alsholm,

thanks for the suggestion. Your approach, once some values for T1 and T2 haven been fixed, effectively allows to compute a solution plot the numerical simulation.

However, I wonder why Maple does not propose a solution when Ta and T2 are left as parameters.

Furthermore, I cannot assume T1+T<T2. Indeed, once the system solved for some symbolic T1 and T2, I should take the limits T1 to 0 (or some other constant value; since taking 0 results in a division by 0), and T2 to (T+T1).

On the other hand, why do you drop the case t<=0, where the piecewise part is 0? The same question applies to t>T2.

Although having a plot to know the behaviour of U2 and L2 is quite interesting, I am interested in having the expression for the solutions of U2 and L2.

Thanks,

jon

@jonlg 

Dear Carl,

tahnks for giving it a try.

The values were already in the first worksheet, as well as the second, but just in case:

r := .25;
m := 6.0;
k := 3.0;
l := 1.2;

Thanks,

jon

Hi,

in the meantime, I further investigated the plot of the worksheet, and verified that it will not work as expected.

This worksheet fixes the issue, taking into account that I the maxG variable is a list of lists: MaplePrimes_malaria_param_variation_2.mw

Thanks again,

jon

@Preben Alsholm 

Dear Preben Alsholm,

yep, that worked. Thanks.

Among ohter things, I thought that the command

ev := ~[LinearAlgebra:-Eigenvalues](Jacobevals)

would take care of evaluation the Jacobian for all parameters given an array, instead of specifying each parameter manually by means of

eval(Jacobevals, {phi = .5, theta = 5})

Still don't know how to handle the direction fields, nullcline computation and their plots: MaplePrimes_Tumour_model_phi_theta_variation.mw

In order to display the dfieldplots and phaseportraits for each parameter, do I need to generate a sequence of plots?

Thanks,

jon

@Axel Vogt 

Axel,

many thanks for your endeavor. A little bit overwhelming; I couldn't imagine the result. I didn't know about Gradsteyn & Ryzhik's integral tables.

Kind regards,

jon

@Carl Love

Yes, it was due to the use of wrong quotation marks. I surely thought of back quotes as being simple quotes.

Thanks for the spelling correction as well.

And sorry for not having sent the whole worksheet. I just thought that the issue did not need it.

Kind regards,

jon

@Carl Love 

Dear Carl,

yep, the solutions you proposed both worked fine.

Thanks again for your endeavor, patience and advice.

jon

@Axel Vogt 

Dear Axel,

very smart solution. I will need to double check.

Yes, I guess we can assume k>0.

Not sure whether the second integral is "that easy", since it is the product of the first (whose expression is somehwat complicated) with an exponential expression that has led you to this not too easy development.

In this case, the questions comes from an simulation on the LQ model for cancer treatment. The ultimate goal of solving these integrals is to get an expression for the G(t) function, which is the generalized Lea-Catcheside factor, which has the general expression:

​​

​​

where D(t) is the dose function, and dotD(t)= dD(t)/dt is the dose rate function.

For the current case, integrating the dose rate function at issue and substituting, I get the expression of G(t) that I would like Maple to integrate:

I hope this makes sense.

Thanks again,

jon

@Carl Love 

Dear Carl Love,

thanks.

No preferences, and I agree that most computer languages accept exp(x). It was may be because in the meantime I have been typing in LaTeX as well, and at some point I have introduced that syntax in my worksheet.

Kind regards,

jon

@Markiyan Hirnyk 

Thanks, Markiyan, but I need not to set the values for the parameters.

Ineed to look into the way I got the integral expression.

jon

@Carl Love 

Dear Carl,

the angle-bracket form solution yields an Array that cannot be dealt with by the LeastSquares curve fitting method, which was the intended destination of the newly created structure.

But thanks for the tip.

Kind regards,

jon

@Preben Alsholm 

Dear Preben Alsholm,

thanks for your answer.

I see that it actually workd for numerically solving the system and plotting the ODE system solutions.

However, for your solution I see that I should repeat the

res(parameters=[phi=0.5,theta=5]);

statement within a loop, and varying the parameters, in order to get all solutions evaluated. Besides, I would need some sort of variable to store all solutions so that I can do:

plots:-odeplot(res[n],[[t,x(t)],[t,100*y(t)]],0..10);

being n an index, in order to plot all solutions.

Is that right?

Ain't there an easier solution?

On the other hand, I have not yet succeeded in doing the same as you did for dsolve for the Jacobian, the steady states, eigenvalues, phase portrait, direction field and nullclines. The last three seem not to accept parameters.

Thanks,

jon

@Carl Love 

Dear Carl Love,

thanks for the tip.

Yes, I need to gain a better knowledged of the structures.

jon