The Joint United Nations Programme on HIV and AIDS (UNAIDS) has set a new 90-90-90 global target for the coverage of anti-retroviral therapy (ART) to be reached by 2020. This would mean that 90% of all people infected with HIV know their status, 90% of them are on ART and 90% of them will have full viral load suppression. Here we first estimate the case reproduction number, R0, for countries in sub-Saharan Africa and for India using data on the rate at which the prevalence of HIV increased at the start of the epidemic and the life expectancy of people living with HIV who are not on ART. R0 determines the magnitude of the control problem, that is to say, the extent to which transmission must be reduced to eliminate HIV. We show that in sub-Saharan Africa the median value of R0 is 4.6 and in all but five countries R0 is less than 6.3. If the 90-90-90 target is reached, 73% of all those living with HIV will have full viral load suppression. If this is maintained it should guarantee elimination in 70% of all countries in sub-Saharan Africa and will reduce R0 to less than 2 in the remaining 12 countries, making elimination easy to achieve by increasing the availability of other high impact methods of prevention.