Timeline for (In)Stability of equilibrium points depicted in a vector plot?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Jul 7, 2021 at 10:58 | vote | accept | Math | ||
| Jul 7, 2021 at 10:57 | history | bounty ended | Math | ||
| Jul 6, 2021 at 14:45 | comment | added | Math | I meant, how do we find the numerical values at the intersection points? I will add the addendum today, but the formatting will crash again so hopefully you can sort it out again. | |
| Jul 1, 2021 at 19:42 | comment | added | Chris K |
@Math Reducing the dimension of the system is usually a great idea when possible. If you want to use the phase plane, that basically requires a two-dimensional system (since it's a plane). I found the intersections in model i) using SolveEcoEq[] but it is a little weird due to the degeneracy, so I put those in manually.
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| Jul 1, 2021 at 15:07 | comment | added | Math | Actually, never mind, I will switch all my models to the SI plane. Also in model (i) how do you find the exact points of intersection in both plots? I will add the addendum on Monday. | |
| Jul 1, 2021 at 11:27 | comment | added | Math | Your answer makes perfect sense, but could you work on the full system? I'm sure it wont be difficult to adjust. This is because I consider other models too so I can apply the same technique provided here to the other models. I will also attach a model including vital dynamics as an addendum so that you can check whether what I did is correct. | |
| Jun 30, 2021 at 16:12 | comment | added | Chris K | I should add, you have the zero eigenvalues because you work on the full system and I don't have them in model (ii) because I have eliminated $R$. | |
| Jun 30, 2021 at 16:04 | history | edited | Chris K | CC BY-SA 4.0 |
fixed formatting
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| Jun 30, 2021 at 16:00 | comment | added | Chris K | @Math I tried to clarify my answer. I made the total-population constraint line pink in model (i), to distinguish it from the isoclines. The total-population constraint doesn't show up in model (ii), because we use it to eliminate $R$ to make the system two-dimensional. I extended the axes in the no-disease case to show the other equilibrium, but it's biologically meaningless ($S>N$ and $I<0$ don't make biological sense). Finally, since you can now see both equilibria in every plot, there's no need for separate figures for each equilibrium (in fact, it's nice to see the global picture). | |
| Jun 30, 2021 at 15:57 | history | edited | Chris K | CC BY-SA 4.0 |
addressed some questions
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| Jun 30, 2021 at 15:33 | comment | added | Math | Also, the total population line(blue line) isn't a linear in model (ii) (stable focus plot), why? | |
| Jun 30, 2021 at 14:40 | comment | added | Math | Also, in model (ii), we have a saddle point when $\beta = 0.95$, $\gamma=1$ and $\xi=0.5$ | |
| Jun 30, 2021 at 14:17 | comment | added | Math | This is nice, however can we show all four vector plots for say part (i)? stable and unstable plots for both $e_1$ and $e_2$ for a given $R_0$? Currently we only see the respective Vector plots as a result of our inputs. | |
| Jun 30, 2021 at 3:04 | history | edited | Chris K | CC BY-SA 4.0 |
added 89 characters in body
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| Jun 30, 2021 at 2:57 | history | answered | Chris K | CC BY-SA 4.0 |