The effect of delayed death in HIV/AIDS models

Figures & data

Table 1. Description and values of parameters of the model.

Parameter	Description	Units	Baseline	Source
Λ	Recruitment rate of individuals into the susceptible population	people year^−1	200	Estimate
$r_1$	Transmission rate in the primary stage	year^−1	4.0	Estimate
$r_2$	Transmission rate in the asymptomatic stage	year^−1	$r_1/12$	[16, 19, 22]
μ	Natural mortality rate	year^−1	$0.02$	[24]
ρ	Progression rate from primary to asymptomatic stage	year^−1	$6.0$	[15, 23]
γ	Mortality rate due to disease	year^−1	$0.1$, variable	Estimate
τ	Survival period of infected individuals	year	10, variable	Estimate

Figure 1. Effect of the survival periods, τ, for the model with delay in death occurrence. (a) Susceptible people (b) Proportion of infected people in the primary stage, $y_1$ (c) Proportion of infected people in the asymptomatic stage, $y_2$ (d) AIDS mortality rates and (e) Total population. Parameters: $r_1=4.0$, $r_2=r_1/12$, $\mu =0.02$, $\mathrm{\Lambda }=200$, $\rho =6.0$ year⁻¹, and $\gamma =0.1$ year⁻¹.

Figure 2. Effect of the death rate, γ, for the model without delay in the occurrence of deaths. (a) Susceptible people (b) Proportion of infected people in the primary stage, $y_1$ (c) Proportion of infected people in the asymptomatic stage, $y_2$ (d) AIDS mortality rates and (e) Total population. Parameters: $r_1=4.0$, $r_2=r_1/12$, $\mu =0.02$, $\mathrm{\Lambda }=200$, and $\rho =6.0$ year⁻¹.

Figure 3. A comparison between the model with and without delay. (a) Susceptible people (b) Proportion of infected people in the primary stage, $y_1$ (c) Proportion of infected people in the asymptomatic stage, $y_2$ (d) AIDS mortality rates and (e) Total population. Parameters: $r_1=4.0$, $r_2=r_1/12$, $\mu =0.02$, $\mathrm{\Lambda }=200$, $\rho =6.0$year⁻¹, $\gamma =0.1$, and $\tau =10$.

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