Table 2.

Estimated parameters with migration together with their uncertainties.

Parameter description	Symbol	Estimates	95% CI
HIV transmissibility	$\beta$	6.0786e-01	(6.0780e-01, 6.0792e-01)
Rate of HIV progression to AIDS	$\alpha$	7.4165e-02	(7.4139e-02, 7.4192e-02)
Natural mortality rate	$d$	3.0475e-01	(3.0472e-01 3.0477e-01)
Recruitment rate of birth	$b$	8.6480e-09	(5.1205e-09 1.2175e-08)
HIV mortality rate	$\mu$	4.3164e-09	(-3.9676e-05, 3.9684e-05)
AIDS mortality rate	$\epsilon$	4.3603e-05	(3.3791e-05, 5.3414e-05)
Proportion of migrants recruited into $S$	$\delta$	1.5572e-01	(1.5561e-01, 1.5583e-01)
Proportion of migrants recruited into $I$	${\delta }_1$	6.3773e-04	(6.3727e-04, 6.3818e-04)
Proportion of migrants recruited into $A$	${\delta }_2$	1.6611e-08	(-8.0299e-07, 8.3621e-07)
The rate migrant at which leaves the population	$\phi$	3.0110e-02	(3.0083e-02, 3.0137e-02)