Optimal strategy for controlling the spread of HIV/AIDS disease: a case study of South Africa

Figures & data

Figure 1. A schematic diagram for the spread of HIV.

Table 1. Parameters used in the model.

Parameter	Description
Λ	Recruitment rate into the S class
d	Natural death rate
β1	Transmission rate for contact with the H class
β2	Transmission rate for contact with the P class ()
k 1	Progression rate from the H class into the P class
k 2	Progression rate from the P class into the A class ( k 1<k 2 )
u 1	Proportion of susceptible individuals who changed their sexual habits per unit time
u 2	Proportion of the P class receiving ARV treatment per unit time
u 3	Proportion of the A class receiving ARV treatment per unit time
δ1	Disease-induced death rate for AIDS individuals
δ2	Disease-induced death rate for the T class ()

Table 2. Parameter values obtained using data from South Africa.

Parameter	Units	Value	Reference
Λ	Population/year	1.04	3 and estimate
d	yr^−1	0.0196	28
β1	yr^−1	0.11	Estimate
β2	yr^−1		10 and estimate
k 1	yr^−1	0.198	10 and estimate
k 2	yr^−1	0.4621	10 and estimate
u 1	yr^−1		Variable
u 2	yr^−1		Variable
u 3	yr^−1		Variable
δ1	yr^−1	0.0909	Estimate
δ2	yr^−1	0.0667	Estimate

Figure 2. Population of the different disease classes with u ₂ ≈ 0 and u ₃=0.5.

Figure 3. Population of the disease-free classes (S, R) with u ₂ ≈ 0 and u ₃=0.5.

Figure 4. Population of the different disease classes with u ₂=0.5 and u ₃ ≈ 0.

Figure 5. Population of the disease-free classes (S, R) with u ₂=0.5 and u ₃ ≈ 0.

Figure 6. The disease prevalence for each of the two scenarios.

Figure 7. The disease incidence for each of the two scenarios.

Figure 8. Control u ₁ for the two scenarios.

Figure 9. Control u ₂ for the two scenarios.

Figure 10. Control u ₃ for the two scenarios.

Dorrington , R. , Johnson , L. , Bradshaw , D. and Daniel , T. The demographic impact of HIV/AIDS in South Africa: National and provincial indicators for 2006 , Cape Town : Centre for the Actuarial Research, South African Medical Research Council and Actuarial Society of South Africa .

 Google Scholar

UNAIDS/WHO . Epidemiological fact sheet on HIV and AIDS: Core data on epidemiology and response. South Africa 2008 Update Available at www.unaids.org or www.who.int/hiv

 Google Scholar

Granich , R. M. , Gilks , C. F. , Dye , C. , De Cock , K. M. and Williams , B. G. “ Universal voluntary HIV testing with immediate antiretroviral therapy as a strategy for elimination of HIV transmission: A mathematical model ” . The Lancet . published online 26 November (2008), doi:10.1016/S0140-6736(08)61697-9

 Google Scholar