1. DEDiscover Differential Equation Modeling Solution CANGLIN WU June-18-2007

2. 2007 Pittsburgh Workshop Canglin Wu 2 DEDiscover Differential Equation Modeling Solution DEDiscover is a cross-platform software tool for building and understanding differential equation models, with special attention to the features necessary for modeling the immune system and viral infection.

3. June-18-20072007 Pittsburgh Workshop Canglin Wu 3 DEDiscover Differential Equation Modeling Solution General Features Cross-platform: Windows, Linux and Mac OS Import models and export standard data and image formats (e.g. CellML, SBML, PNG, JPEG, PS, EPS etc.) Plug in architecture

4. June-18-20072007 Pittsburgh Workshop Canglin Wu 4 DEDiscover Differential Equation Modeling Solution Model Support Standard mathematical notations, plus macros, indicator functions, time-varying parameters, history functions, and constraints ODE and DDE models Pre-defined or user specified models

5. June-18-20072007 Pittsburgh Workshop Canglin Wu 5 DEDiscover Differential Equation Modeling Solution Model input and solver selection

6. June-18-20072007 Pittsburgh Workshop Canglin Wu 6 DEDiscover Differential Equation Modeling olution Parameters and initial conditions

7. June-18-20072007 Pittsburgh Workshop Canglin Wu 7 DEDiscover Differential Equation Modeling Solution Simulation Support Several ODE and DDE solvers Real-time solutions allow interactive exploration Tabular and Graphical display of results Customizable displays

8. June-18-20072007 Pittsburgh Workshop Canglin Wu 8 DEDiscover Differential Equation Modeling Solution Simulation result - Combined plot

9. June-18-20072007 Pittsburgh Workshop Canglin Wu 9 DEDiscover Differential Equation Modeling Solution Simulation result - Individual plot

10. June-18-20072007 Pittsburgh Workshop Canglin Wu 10 DEDiscover Differential Equation Modeling Solution Simulation result - Table

11. June-18-20072007 Pittsburgh Workshop Canglin Wu 11 DEDiscover Differential Equation Modeling Solution Estimation Support Several estimation & optimizer methods Point estimates and confidence intervals Estimation of both initial conditions and parameters Properly fits data with experiment, treatment, and technical replicates Interactive display and control of estimation progress

12. June-18-20072007 Pittsburgh Workshop Canglin Wu 12 DEDiscover Differential Equation Modeling Solution Formula Syntax Dependent variable, dEP/dt Delay variable, TE(t-tau_T) Temporary variable like MACRO, suggest use temp_ as prefix, for example temp_var= k*T1*V Suggest capital for variable and low- case for parameter

13. June-18-20072007 Pittsburgh Workshop Canglin Wu 13 DEDiscover Differential Equation Modeling Solution Formula Syntax Indicator function I(tau_T,100)(t) tau_T<I<100 I[tau_T,100)(t) tau_T<=I<100 I(tau_T,100](t) tau_T<I<=100 I[tau_T,100](t) tau_T<=I<=100 Initial condition in formula, D(0) Comment, // for comment one line, /* */ for comment multiple lines

14. June-18-20072007 Pittsburgh Workshop Canglin Wu 14 DEDiscover Differential Equation Modeling Solution Formula Syntax Case insensitive, V and v are same variable NOT two variables DO NOT use * as a part of variable name, reserved for multiple operation DO NOT use T or t as variable name, reserved for independent variable

15. June-18-20072007 Pittsburgh Workshop Canglin Wu 15 DEDiscover Differential Equation Modeling Solution Reserved Words T, t, //, /*, */, +, -, *, /, =,,,., (, ),, ‘, ^, e, log, sin, cos, tan etc You CAN NOT use reserved word as variable and parameter name

16. June-18-20072007 Pittsburgh Workshop Canglin Wu 16 DEDiscover Differential Equation Modeling Solution Operator + Add - Subtract * Multiply / Divide % Modulus ^ Power: y = x ^ 2( ) () Parenthesis. For example: (2 + 3) * 5

17. June-18-20072007 Pittsburgh Workshop Canglin Wu 17 DEDiscover Differential Equation Modeling Solution Math functions sin(x) Calculate sine sinh(x)Calculate hyperbolic sine Cos(x) Calculate cosine Cosh(x) Calculate hyperbolic cosine tan(x) Calculate tangent tanh(x) Calculate hyperbolic tangent asin(x) Calculate arcsine acos(x) Calculate arccosine atan(x) Calculate arctangent atan2(x, y) Calculate arctangent with two parameters to preserve quadrant angle bessj(n, v) Bessel function of the first kind. n isorder and v is input value. bessy(n, v).Bessell function of the second kind. nis order and v is input value hypot(a,b) Calculate hypotenuse of right triangle

18. June-18-20072007 Pittsburgh Workshop Canglin Wu 18 DEDiscover Differential Equation Modeling Solution Math functions abs(x) Return absolute value max(x) Return larger of two values min(x) Return smaller of two values sqrt(x) Find square root Ceil(x) Find integer ceiling floor(x) Calculate hypotenuse of right triangle exp(x) Calculate exponential function: ex log(x) Calculate natural logarithm log10(x) Calculate base-10 logarithm rand(x) Get pseudorandom number between 0 and 1 srand(x) Initialize pseudorandom series

19. June-18-20072007 Pittsburgh Workshop Canglin Wu 19 DEDiscover Differential Equation Modeling Solution Download Log in CBIM website first Download at http://cbim.urmc.rochester.edu/software Install DEDiscover package in your computer

20. June-18-20072007 Pittsburgh Workshop Canglin Wu 20 DEDiscover Differential Equation Modeling Solution DEDicover DEMO

21. June-18-20072007 Pittsburgh Workshop Canglin Wu 21 DEDiscover Differential Equation Modeling Solution Acknowledgment NIAID/NIH grant NO1 AI50020 Center for Biodefense Immune Modeling Design : Hulin Wu, Gregory Warnes, Dongwen Wang Program: Hongyu Miao, Alain Leblanc Model: Alan Perelson, HY Lee, SY Lee Other: Jeanne Holden-Wiltse, Temple Herlong

22. June-18-20072007 Pittsburgh Workshop Canglin Wu 22 DEDiscover Differential Equation Modeling Solution Thanks Q & A