| Literature DB >> 24348744 |
E Lungu1, T J Massaro2, E Ndelwa3, N Ainea3, S Chibaya3, N J Malunguza4.
Abstract
We formulate a deterministic system of ordinary differential equations to quantify HAART treatment levels for patients co-infected with HIV and Kaposi's Sarcoma in a high HIV prevalence setting. A qualitative stability analysis of the equilibrium states is carried out and we find that the disease-free equilibrium is globally attracting whenever the reproductive number ℛk < 1. A unique endemic equilibrium exists and is locally stable whenever ℛk > 1. Therefore, reducing ℛk to below unity should be the goal for disease eradication. Provision of HAART is shown to provide dual benefit of reducing HIV spread and the risk of acquiring another fatal disease for HIV/AIDS patients. By providing treatment to 10% of the HIV population, about 87% of the AIDS population acquire protection against coinfection with HIV and Kaposi's Sarcoma (KS). Most sub-Sahara African countries already have programmes in place to screen HIV. Our recommendation is that these programmes should be expanded to include testing for HHV-8 and KS counseling.Entities:
Mesh:
Year: 2013 PMID: 24348744 PMCID: PMC3855956 DOI: 10.1155/2013/753424
Source DB: PubMed Journal: Comput Math Methods Med ISSN: 1748-670X Impact factor: 2.238
Figure 1Model flow diagram.
Figure 2(a) 3D plot of ℛ against the rates of KS manifestation for infected and pre-AIDS classes for variable values of ϵ 1 and ϵ 2, all other parameters constant as in Table 1, (b) contour plot map of ℛ against ϵ 1 and ϵ 2, all other parameters constant as in Table 1, (c) 3D plot of ℛ against the rates of ART administration for infected and pre-AIDS classes for variable values of ϕ 1 and ϕ 2, all other parameters constant as in Table 1, and (d) contour plot map of ℛ against ϕ 1 and ϕ 2, all other parameters constant as in Table 1.
Parameter values and their estimates.
| Parameter | Symbol | Value | Source |
|---|---|---|---|
| HIV rate of transmission |
| 0.4801* | Baggaley et al. [ |
| Boily et al. [ | |||
| Death due to AIDS |
| 0.333 | Malunguza et al. [ |
| Mukandavire et al. [ | |||
| Death due to AIDS with KS |
| 0.067* | Malunguza et al. [ |
| Mukandavire et al. [ | |||
| Rate of KS acquisition among HIV-infected cohort |
| 0.001 | Assumed |
| Rate of KS acquisition among pre-AIDS cohort |
| 0.002 | Assumed |
| Rate of KS acquisition among AIDS cohort |
| 0.003 | Assumed |
| Relative HIV infectiousness of an HIV-infected individual |
| 0.8 | Assumed |
| Relative HIV infectiousness of a coinfected individual |
| 1.1 | Assumed |
| Relative HIV infectiousness of a pre-AIDS individual |
| 1.2 | Assumed |
| Relative HIV infectiousness of an AIDS individual |
| 1.3 | Assumed |
| Recruitment rate of sexually mature individuals | Λ | 800* | Barley et al. [ |
| Malunguza et al. [ | |||
| Mukandavire et al. [ | |||
| Natural mortality rate |
| 0.02 | Mukandavire et al. [ |
| Treatment rate of infected and coinfected cohorts |
| Varies | Assumed |
| Treatment rate of pre-AIDS and pre-AIDS coinfected cohorts |
| Varies | Assumed |
| Natural progression to pre-AIDS |
| 0.01 | Assumed |
| Rate of acute KS development in coinfected cohort |
| 0.0001 | Assumed |
| Rate of acute KS development in pre-AIDS coinfected cohort |
| 0.0002 | Assumed |
| Rate of acute KS development in AIDS coinfected cohort |
| 0.0003 | Assumed |
| Natural progression to AIDS |
| 0.1 | Mukandavire et al. [ |
| Natural progression to AIDS after treatment |
| 0.1 | Assumed |
*Denotes a parameter obtained by modifying a value in the given source.
Figure 3Epidemic curves for our model with the following treatment scenarios: (a) no treatment (ϕ 1 = ϕ 2 = 0), (b) 1% treatment level (ϕ 1 = ϕ 2 = 0.01), and (c) 10% treatment level (ϕ 1 = ϕ 2 = 0), (d) treatment rate versus AIDS population without coinfection. A treatment level of 10% is sufficient at minimizing endemic populations in all the infective, untreated classes at the equilibrium.