Estimating seasonal drivers in childhood infectious diseases with continuous time and discrete-time models

2010 ◽  
Author(s):  
D P Word ◽  
G H Abbott ◽  
D Cummings ◽  
C D Laird
Keyword(s):  
Infectious Diseases ◽  
Discrete Time ◽  
Continuous Time ◽  
Discrete Time Models

Discretization of Nonautonomous Nonlinear Systems Based on Continualization of an Exact Discrete-Time Model

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Triet Nguyen-Van ◽  
Noriyuki Hori
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Van Der Pol Oscillator ◽  
Discrete Time System ◽  
Time System ◽  
Time Model ◽  
Forward Difference ◽  
Discrete Time Models

An innovative approach is proposed for generating discrete-time models of a class of continuous-time, nonautonomous, and nonlinear systems. By continualizing a given discrete-time system, sufficient conditions are presented for it to be an exact model of a continuous-time system for any sampling periods. This condition can be solved exactly for linear and certain nonlinear systems, in which case exact discrete-time models can be found. A new model is proposed by approximately solving this condition, which can always be found as long as a Jacobian matrix of the nonlinear system exists. As an example of the proposed method, a van der Pol oscillator driven by a forcing sinusoidal function is discretized and simulated under various conditions, which show that the proposed model tends to retain such key features as limit cycles and space-filling oscillations even for large sampling periods, and out-performs the forward difference model, which is a well-known, widely-used, and on-line computable model.

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