Abstract
Biological processes such as contagious disease spread patterns and tumor growth dynamics are modelled using a set of coupled differential equations. Experimental data is usually used to calibrate models so they can be used to make future predictions. In this study, numerical methods were implemented to approximate solutions to mathematical models that were not solvable analytically, such as a SARS model. More complex models such as a tumor growth model involve high-dimensional parameter spaces; efficient numerical simulation techniques were used to search for optimal or close-to-optimal parameter values in the equations. Runge-Kutta methods are a group of explicit and implicit numerical methods that effectively solve the ordinary differential equations in these models. Effects of the order and the step size of Runge-Kutta methods were studied in order to maximize the search accuracy and efficiency in parameter spaces of the models. Numerical simulation results showed that an order of four gave the best balance between truncation errors and the simulation speed for SIR, SARS, and tumormodels studied in the project. The optimal step size for differential equation solvers was found to be model-dependent.
Highlights
It has been observed that virus-originated diseases exhibited similar spread and control patterns [1,2]
A tumor cell growth model usually involves coupled differential equations with a high dimensional parameter space, which is the result of many factors involved in the tumor growth dynamics [9]
A mathematical model for SARS was simulated to study the effect of different quarantine and isolation control methods on the disease subpopulation dynamics
Summary
It has been observed that virus-originated diseases exhibited similar spread and control patterns [1,2]. Once the quarantine and isolation methods, as well as strict health precautions, went into effect, the disease started to die out During this process, it has been observed that SARS, like certain other virusoriginated diseases, exhibited similar spread and control patterns. A calibrated SARS model has the potential to give more accurate predictions on virus-originated disease spread and control patterns in the future. GAs were invented based on the natural evolution process while the PSO method was inspired by the social behaviour of bird flocking or fish schooling, the collective intelligent behaviours of individuals who interact with each other and their environment Both GAs and the PSO method help to calibrate the model to fit experimental data within tolerable error ranges in a reasonable time frame. The final section concludes the paper and discusses possible future work
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