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An efficient numerical method to evaluate the cost of quarantine strategies for new emerging diseases

Kailash Patidar



Abstract: A classical model illustrating the quarantine and isolation procedure in connection to the recent SARS outbreak is considered. Due to the complex structure of the model, it is difficult to solve analytically and hence it is essential to look for some suitable numerical integrators. We show that while usual explicit approximation methods (for example, forward Euler) is practically irrelevant, a fully implicit method, for instance, backward Euler has various other drawbacks. To this end, we design a novel numerical method which is asymptotically/dynamically consistent with the continuous model and also overcomes the draw backs of the other methods mentioned above. The method is analyzed for stability and convergence. Numerical results obtained with this approach are compared with those obtained via conventional MATLAB ode solvers. (1) Mathematical and Theoretical Biology Institute, Arizona State University, P.O. Box 871804, Tempe, AZ 85287-1804, USA (2) Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa