Optimal control of an HIV infection model with logistic growth, celluar and homural immune response, cure rate and cell-to-cell spread

Boundary Value Problems

Table 2 The values of the parameters in the HIV mathematical model

Parameters	Units	Column 1	Column 2	Column 3	Column 4	References
r	\(day^{-1} \)	2	2	2	2	Assumed
m		15,000	100,000	5 × 10⁴	300,000	Assumed
\(\beta _{1} \)	\(ml . (virion . day)^{-1} \)	4.8 × 10⁻⁷	4.8 × 10⁻⁷	4.8 × 10⁻⁷	4.8 × 10⁻⁷	[38]
\(\beta _{2} \)	\(ml . (virion . day)^{-1} \)	4.7 × 10⁻⁷	4.7 × 10⁻⁷	4.7 × 10⁻⁷	4.7 × 10⁻⁷	[38]
α	\(cells^{-1} . ml \)	0.001	0.001	0.001	0.001	[39–42]
ρ	\(day^{-1} \)	0.01	0.01	0.01	0.01	[39–42]
d	\(day^{-1} \)	0.02	0.02	0.02	0.02	[39–42]
δ	\(day^{-1} \)	0.5	0.5	0.5	0.5	[39–42]
\(\rho _{1} \)	\(ml . (cells . day)^{-1} \)	0.001	0.001	0.001	0.001	[39–42]
n	ml.virion	1200	1200	1200	1200	[39–42]
μ	\(day^{-1} \)	3	3	3	3	[39–42]
\(\rho _{2} \)	\(ml . (virion . day)^{-1} \)	0.5	0.001	0.001	0.001	[43]
\(c_{1} \)	\(ml . (cells . day)^{-1} \)	0.021	0.021	0.021	0.021	Assumed
\(b_{1} \)	\(day^{-1} \)	0.2	0.2	0.2	0.2	[39–42]
\(c_{2} \)	\(ml . (virion . day)^{-1} \)	10⁻¹¹	10⁻¹¹	10⁻⁴	10⁻⁴	[43]
\(b_{2} \)	\(day^{-1} \)	0.1	0.1	0.01	0.1	[43]