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A theoretical model for the transmission dynamics of HIV/HSV-2 co-infection in the presence of poor HSV-2 treatment adherence

A. Mhlanga
A. Mhlanga
   | Dec 31, 2018
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Published Online: Dec 31, 2018
Page range: 603 - 626
Received: Oct 07, 2018
Accepted: Dec 31, 2018
DOI: https://doi.org/10.2478/AMNS.2018.2.00047
Keywords
© 2018 A. Mhlanga, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fig. 1

Structure of model.
Structure of model.

Fig. 2

Graphs of the numerical simulation of the optimality system, showing the propagation of (a) HIV cases only and (b) AIDS cases over a period of 36 months.
Graphs of the numerical simulation of the optimality system, showing the propagation of (a) HIV cases only and (b) AIDS cases over a period of 36 months.

Fig. 3

Graphs of the numerical simulation of the optimality system, showing the propagation of (a) individuals dually infected with HIV and acute HSV-2, also under HSV-2 anti-viral treatment and (b) individuals dually infected with HIV and acute HSV-2, also not under HSV-2 anti-viral treatment, over a period of 36 months.
Graphs of the numerical simulation of the optimality system, showing the propagation of (a) individuals dually infected with HIV and acute HSV-2, also under HSV-2 anti-viral treatment and (b) individuals dually infected with HIV and acute HSV-2, also not under HSV-2 anti-viral treatment, over a period of 36 months.

Fig. 4

The optimal control graphs for the two controls, namely, monitoring and counselling individuals infected with HSV-2 only (u1) and monitoring and counselling individuals dually infected with HSV-2 and HIV (u2), over a period of 36 months.
The optimal control graphs for the two controls, namely, monitoring and counselling individuals infected with HSV-2 only (u1) and monitoring and counselling individuals dually infected with HSV-2 and HIV (u2), over a period of 36 months.

Model parameters and their baseline values. The time unit is in months

DefinitionSymbolBaseline values (Range)Source
Effective contact rate for HSV-2 infectionβI0.2[1, 25]
Effective contact rate for HIV infectionβH0.3 (0.11-0.95)[30]
Rate of acute HSV-2 becoming latentκ12.3805(2.083-2.678)[26]
Rate of acute HSV-2 and HIV infected becoming latentκ21.683(1.458-1.875)[26]
Treatment quitting rateδ10.3[26, 27]
Treatment quitting rate (dually infected)δ20.3Assumed
Proportion of HSV-2 patients who successfully complete treatmentθ10.7(0-1)Assumed
Proportion of patients who successfully complete treatment (dually infected)θ20.8(0-1)Assumed
Reactivation rate with an effect of treatment (HSV-2 only)γ(1)(ψ)Varies[1]
Reactivation rate with an effect of treatment (dually infected)γ(2)(ψ)Varies[1]
Baseline reactivation rate of latent HSV-2γ0(1)$\begin{array}{} \gamma_0^{(1)} \end{array} $(ψ)0.339-0.436[26]
Baseline reactivation rate of latent HSV-2 (dually infected)γ0(2)$\begin{array}{} \gamma_0^{(2)} \end{array} $(ψ)0.365-0.469[26]
Enhanced susceptibility of people with acute HSV-2 to HIV infectionσ2.7-3.1[29]
Enhanced susceptibility to HSV-2 infection by HIV infectivesφ≥ 1[1]
Treatment rate of acute HSV-2ψVaried[1]
Rate of progression from HIV to AIDSϕ0.0104[26]
Average sexual lifespanμ0.004(0.003-0.005)[25, 26]
AIDS-related death ratev0.03[32]
Modification parameterα1(0−1)Assumed
Modification parameterα2(0−1)Assumed
Modification parameterη1(0−1)Assumed
Modification parameterη2(0−1)Assumed
Modification parameterτ(0−1)Assumed
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