Simulation of COVID-19 Spread and Control Dynamics

Research Group at Shepherd University - Dr. Qing Wang (Mathematics, PI), Mr. John Sheranko (Science/Biology), Ms. Christine Wang (Computer Simulation/App Site Maintenance).

Goal of Simulation

Find the close-to-optimal, hopefully the optimal, parameter set in a high-dimensional parameter space using a computationally tractable method. Please see paper for the model. Test sets derived from CDC and JHU.

Parameter Set Optimization

Genetic Algorithm. Encode with the parameter set. Evolve using crossover and mutation. For each generation, the ODE set is solved for each individual and the fitness function value (variance here) is calculated. The top half is passed to the next generation. Note the best individual in each generation is free from mutation. Crossover point(s) and mutation rate can be dynamically adjustable parameters so the algorithm can move more efficiently in the large parameter space and hopefully not get trapped in not-so-good local minimums.

Initial Value ODE Solvers

Runge-Kutta (order 4). Adams-Moulton formulas (non-stiff problems). Backward differentiation formulas (stiff problems). Any ODE solver should be implemented in the most efficient way due to the amount of calls in the genetic method. The ODE solver is the computational bottleneck of the simulation.

Please note: All variable and parameter values are equally weighted during the initial phase. The relative weights can be changed easily.

Design and Implementation

Parameter ranges, initial values, and simulation parameters can be specified on the interface. Final converged or time-up parameter values and the numerical solution to ODEs are saved in a text file and used for analysis and drawing.

Please note that functional curves for variables can be drawn using the saved data file. There are quite a few variables and they have different units so they can not be drawn in the same graph on the simulation interface.

Visual Basic Power Pack may be needed to run the application.