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I am new on this forum and I hope that I will provide useful answer to mathematics problems that people might have to face in the future. Also, I do want to meet mathematicians from all over the world aha

I am currently discovering Matlab Simulink to simulate a system of non-linear differential equations. I succeeded in building a block-structure system. However, there is no one in my close circle that can provide me constructive feedback on it because they do not have, unfortunately, the skills to do so.

The system that I am trying to simulate came from :

Portaluri, Alessandro & Paparella, Francesco & Alma, Alberto & Lessio, Federico. (2020). A mathematical model for Flavescence dorée epidemiology.

There is also a more complete version in :

Lessio, Federico & Portaluri, Alessandro & Paparella, Francesco & Alma, Alberto. (2014). A Mathematical Model of Flavescence Dorée Epidemiology. Ecological Modelling. 312. 10.1016/j.ecolmodel.2015.05.014.

Here is the system :

With, $$ \begin{aligned} S_0 &= 5800 \\ I_0 &= 200 \\ G_0 &= 0 \end{aligned}\quad \begin{aligned} D &= 6000 \\ k_i,~~\epsilon,~~q &= \text{ constants} \\ \tau &= 1 \end{aligned} $$ So, \begin{align} S' &= -qS(pI+\epsilon)^2+k_1I+k_4G \\ I' &= ~~qG(pI+\epsilon)^2-k_1I-k_3I \\ G' &= -qG(pI+\epsilon)^2-k_4G+\tau^{-1}(D-S-I-G) \end{align}

Here is the Simulink block model that I built.

block diagram

Please feel free to give me some feedback and criticism, so I can know if I produced bad work or not.

Thanks you all,

Hugo

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8mo1
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  • The diagram looks correct, is there any reason to suspect an error? You have aligned the integrators vertically, it would probably increase the organization if you could also align the term additions that make up the integrands. Also, shift all term constructions to either side (left if possible, so that the integrators are directly beside the output). /// Is there a special reason that you want to use simulink and not integrate directly with ode45? – Lutz Lehmann Apr 05 '22 at 09:19
  • @LutzLehmann Thanks you sir for your kind answer ! No, there was no reason but I wanted to be sure of the stability of the diagram before keeping on my work :) I am new on Matlab and Simulink seemed to me the easiest way to do that. However, I will take a look to ode45 if you think that it can make the simulation easier to do. – 8mo1 Apr 05 '22 at 09:48
  • Simulink should be more interactive out-of-the-box. But it is also very easy using the same intermediary expressions to compose the ODE function in a similar way to the block diagram. – Lutz Lehmann Apr 05 '22 at 10:11

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