D'Onofrio chemotherapy model - Revision history

ClemensZeile at 13:31, 11 January 2018

2018-01-11T13:31:14Z

← Older revision		Revision as of 13:31, 11 January 2018
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	Image:d'Onofrio 4.png\| Optimal controls and states with parameter set 4.		Image:d'Onofrio 4.png\| Optimal controls and states with parameter set 4.
	</gallery>		</gallery>

			== Variants ==

			* a variant where partial outer convexification is applied on the control and the continous control is replaces by binary controls, see also [[D'Onofrio model (binary variant)]],


	==Source Code==		==Source Code==

2016-07-27T08:26:54Z

2016-06-27T22:07:21Z

Mathematical formulation

2016-06-27T22:07:03Z

Mathematical formulation

2016-06-27T22:04:59Z

Source Code

← Older revision		Revision as of 22:04, 27 June 2016
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	* [[:Category:Muscod \| Muscod code]] at [[D'Onofrio chemotherapy model (Muscod)]]		* [[:Category:Muscod \| Muscod code]] at [[D'Onofrio chemotherapy model (Muscod)]]
	~~<source lang="cpp">~~
	~~/* volume of tumor */~~
	~~rhs[0] = - zetax[0]log(x[0]/x[1])-Fx[0]u1_;~~
	~~/* volume of neighboring blood vessels */~~
	~~rhs[1] = bx[0] - (mu + dpow(x[0],2.0/3.0))x[1] - Gu0_x[1] - etax[1]*u1_;~~
	~~/* amount of anti-angiogetic drug */~~
	~~rhs[2] = u0_;~~
	~~/* amount of cytostatic drug */~~
	~~rhs[3] = u1_;~~
	~~</source>~~

	== References ==		== References ==

2016-06-27T22:04:49Z

Source Code

← Older revision		Revision as of 22:04, 27 June 2016
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	==Source Code==		==Source Code==

	[[:Category:Muscod \| Muscod code]]		* [[:Category:Muscod \| Muscod code]] at [[D'Onofrio chemotherapy model (Muscod)]]
	<source lang="cpp">		<source lang="cpp">
	/* volume of tumor */		/* volume of tumor */

2016-06-27T22:03:07Z

← Older revision		Revision as of 22:03, 27 June 2016
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	<biblist />		<biblist />

			[[Category:MIOCP]]
	[[Category:Medicine]]		[[Category:Medicine]]
	~~[[Category:MIOCP]]~~
	[[Category:ODE model]]		[[Category:ODE model]]
			[[Category:Bang bang]]
			[[Category:Path-constrained arcs]]

2016-04-10T09:28:32Z

Mathematical formulation

2016-04-10T09:28:05Z

Mathematical formulation

← Older revision		Revision as of 09:28, 10 April 2016
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	\begin{array}{llcl}		\begin{array}{llcl}
	\displaystyle \min_{x, u} & x_0(t_f) &+& \alpha \int_{t_0}^{t_f} u_0(t)^2 \text{d}t \\[1.5ex]		\displaystyle \min_{x, u} & x_0(t_f) &+& \alpha \int_{t_0}^{t_f} u_0(t)^2 \text{d}t \\[1.5ex]
	\mbox{s.t.} & \dot{x}_0~~(t)~~ & = & - \zeta x_0~~(t)~~ \text{ln} \left( \frac{x_0~~(t)~~}{x_1~~(t)~~} \right) - F \; x_0~~(t)~~ u_1~~(t)~~, \\		\mbox{s.t.} & \dot{x}_0 & = & - \zeta x_0 \text{ln} \left( \frac{x_0}{x_1} \right) - F \; x_0 u_1, \\
	& \dot{x}_1~~(t)~~ & = & b x_0~~(t)~~ - \mu x_1~~(t)~~ - d x_0~~(t)~~^{\frac{2}{3}}x_1~~(t)~~ - G u_0~~(t)~~ x_1~~(t)~~ - \eta x_1~~(t)~~ u_1~~(t)~~, \\		& \dot{x}_1 & = & b x_0 - \mu x_1 - d x_0^{\frac{2}{3}}x_1 - G u_0 x_1 - \eta x_1 u_1, \\
	& \dot{x}_2~~(t)~~ & = & u_0~~(t)~~, \\		& \dot{x}_2 & = & u_0, \\
	& \dot{x}_3~~(t)~~ & = & u_1~~(t)~~, \\ [1.5ex]		& \dot{x}_3 & = & u_1, \\ [1.5ex]
	& 0 & \leq & u_0~~(t)~~ \leq u_0^{max}, \\		& 0 & \leq & u_0 \leq u_0^{max}, \\
	& 0 & \leq & u_1~~(t)~~ \leq u_1^{max}, \\		& 0 & \leq & u_1 \leq u_1^{max}, \\
	& x_2~~(t)~~ & \leq & x_2^{max}, \\		& x_2 & \leq & x_2^{max}, \\
	& x_3~~(t)~~ & \leq & x_3^{max}.		& x_3 & \leq & x_3^{max}.
	\end{array}		\end{array}
	</math>		</math>

2016-01-28T09:49:51Z

added medicine