Hybrid Taguchi-Differential Evolution Algorithm for Parameter Estimation of Differential Equation Models with Application to HIV Dynamics

Table 1

Comparison of results for the estimated parameters and the performance index with 100 independent runs for the HIV dynamical model.

Approach		Best value	Mean value	Standard deviation
HTDE	𝑆	1.0000	1.0000	0.0003
	𝑑	0.8000	0.8000	0.0003
	𝛽	1.0000	1.0000	0.0002
	𝜇1	0.8000	0.8000	0.0003
	𝑘	1.0000	1.0000	0.0005
	𝜇2	0.01078	0.01079	0.0002
	𝐽	3.62 × 10^-10	2.86 × 10^-9	2.09 × 10^-9
DE	𝑆	1.0209	1.1582	0.2750
	𝑑	0.7636	0.9497	0.2692
	𝛽	1.0034	1.0544	0.1591
	𝜇1	0.7919	0.8877	0.2848
	𝑘	1.0131	1.2349	0.2199
	𝜇2	0.01073	0.10865	0.09900
	𝐽	0.0007924	0.0021460	0.0010318
Transformation 1 proposed by Manseur et al. [22]	𝑆	0.964
	𝑑	0.856
	𝛽	0.928
	𝜇1	0.715	NA	NA
	𝑘	0.98
	𝜇2	0.009
	𝐽	0.0010
Transformation 2 proposed by Manseur et al. [22]	𝑆	0.724
	𝑑	0.582
	𝛽	0.97
	𝜇1	0.3785	NA	NA
	𝑘	0.9409
	𝜇2	0.1058
	𝐽	0.02036
Levenberg-Marquardt method presented by Manseur et al. [22]	𝑆	0.79
	𝑑	0.67
	𝛽	0.85
	𝜇1	0.705	NA	NA
	𝑘	0.88
	𝜇2	0.021
	𝐽	0.07