How to divide different graphs?

Is there anyway to divide this function up, and have the first 4 equations (dSdt(1) to dSdt(4)) computed into one graph and the remaining last 3 equations computed on a separate graph? This is a mathematical modelling question, with dSdt(1) to dSdt(4) representing the one population and dSdt(5) to dSdt(7) representing another population. to = 0; tf = 100; tspan = [to tf]; y0 = [5535002 50 50 0 0 0 0 ]; [t,S] = ode45(@denguefeverODE, tspan, y0); plot(t,S) title('Human Population Without Control') xlabel('Time') ylabel('Susceptible, Exposed, Infected, Recovered') legend('Susceptible', 'Exposed', 'Infected', 'Recovered') function dSdt = denguefeverODE(t,S) Nh = 5535002; Nm = 33210012; uh = 0.0045; um = 0.02941; Pmh = 0.375; Phm = 0.750; beta = 1; nu_h = 0.1666; epsilon_m = 0.1; tau_h = 0.1176; f = 6; dSdt = zeros(7,1); dSdt(1) = uh*Nh - (beta*Pmh*(S(7)/Nh)+uh)*S(1); dSdt(2) = beta*Pmh*(S(7)/Nh)*S(1) - (tau_h+uh)*S(2); dSdt(3) = tau_h*S(2)-(nu_h+uh)*S(3); dSdt(4) = nu_h*S(3)-uh*S(4); dSdt(5) = um*Nm - (beta*Phm*(S(3)/Nh)+um)*S(5); dSdt(6) = beta*Phm*(S(3)/Nh)*S(5); dSdt(7) = epsilon_m*S(6) - um*S(7);

Thank you!

Answer 1

[Star Strider]

I ran your code and tested this (it works). Your figure becomes two figures, each plotting the columns of ‘S’ you want:

figure(1)
plot(t,S(:,1:4))
title('Human Population Without Control')
xlabel('Time')
ylabel('Susceptible, Exposed, Infected, Recovered')
legend('Susceptible', 'Exposed', 'Infected', 'Recovered')

figure(2)
plot(t,S(:,5:7))
title('Human Population Without Control')
xlabel('Time')
ylabel('Susceptible, Exposed, Infected, Recovered')
legend('Susceptible', 'Exposed', 'Infected', 'Recovered')

[Muse Riveria]

Thank you very much!!!

[Star Strider]

My pleasure!

Interesting project, too, and a professional interest of mine. Do you have a reference for it?

[Muse Riveria]

Quite a few actually! Reference for mathematical modelling? Or Dengue fever specifically?

But this model appears quite strange, perhaps it's the data? But the graph for the vector population doesn't make sense. The susceptible population decreases then increases; this isn't supposed to happen. Well, certainly based on my research.

[Muse Riveria]

And another question, if you help me out another time! Would it be possible to incorporate a constant control strategy (c = 0.084) to solve for the equations mentioned above? Whereby the control strategy (c = 0.084) is constant, with application of 8.4% capacity of insecticide 24 hours per day all the time. Following this administration, the number of infected mosquitos and humans should reduce.

Please refer here on the last few pages if need be: http://repositorium.sdum.uminho.pt/bitstream/1822/15161/3/199Dengue_disease_basic_reproduction_number_and_control.pdf

[Star Strider]

The epidemiological modeling. I can find Dengue articles in my professional journals, but my epidemiology background isn’t as robust. Besides, with global warming, Dengue and other arboviruses are going to spread, so understanding its epidemiology is important.

I don’t see ‘c’ in the constants in your equations, and I only briefly looked at the paper (thank you for it), so I cannot respond to that specifically. The level of ‘c’ you want to use (I don’t know what you’re using now) is less than the value that the paper states significantly reduces the mosquito numbers. From a practical standpoint of course, applying insecticide all the time, especially at a concentration less than the paper posits as a value that would reduce the reproduction rate significantly, would favour the emergence of mosquitoes that are insecticide resistant, so you would have to model that as well. (There would also be wider environmental consequences, unless the insecticide was somehow mosquito-specific.) That would be the same for chemical insecticides as for B. thuringiensis, at least from my understanding of its mode of action.

One idea you might consider is to apply both a low concentration of a chemical insecticide together with B. thuringiensis and see if the reproduction rate of the mosquitoes is significantly lower than with one agent alone (as I suspect it would be), but with the significant advantage of the mosquitoes not becoming resistant to both agents simultaneously, possibly eliminating them entirely, at least in the short term (until new ones arrived). This is the principal used in infectious disease (and cancer chemotherapy) to prevent bacteria specifically from becoming resistant to one antibiotic. They might mutate to become resistant to one, but to survive, they have to mutate to resist both simultaneously, and that is extremely rare (although it is emerging, owing to the misuse of antibiotics in certain parts of the world, and their almost completely inappropriate use in ‘factory’ animal operations). I am not certain that has ever been modeled, so I have no idea how to implement it. It could require you to include a probability model of resistance, significantly complicating your study.

[Muse Riveria]

Here are the sources I referred to when attempting to comprehend mathematical modelling:

- http://pythonhosted.org/epigrass/intromodels.html

- http://www.bioss.ac.uk/~glenn/mathmod/seir.pdf

- https://books.google.com.sg/books?id=jtGP_qwD1MgC&pg=PA24&lpg=PA24&dq=why+is+average+life+span+1/%CE%BC&source=bl&ots=xIdpZk3MRX&sig=B-4F1hakG77ZLxD67KsqCO77WWg&hl=en&sa=X&ved=0ahUKEwjzvJ_pg_bJAhUUkI4KHZlWC8MQ6AEIKjAF#v=onepage&q=why%20is%20average%20life%20span%201%2F%CE%BC&f=false

The other ones I used were specifically for dengue fever.

Thank you for the additional information on methods to reduce the reproduction rate of mosquitoes. I guess I will have to conduct further research before proceeding with this project of mine.

Once again,thank you very much for you help!

[Star Strider]

My pleasure!

This has been a genuine education for me, so I thank you as well. I’ll definitely look at those references.