# Exploring Projections for HIV Infection with Pre-Exposure Prophylaxis Usage in a High-Risk Population

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## Abstract

**:**

## Featured Application

**The numerical model may be modified to provide national, state, or local means of monitoring adherence to PrEP protocols, assessing disparities and access to care, and to inform public policy regarding PrEP advocacy.**

## Abstract

## 1. Introduction

## 2. Methods

- The death rates associated with HIV and AIDS have become steady and stable.
- The rate of disease progression from HIV to AIDS is held constant with the acknowledgement that it is likely to decrease over time considering current data trends.
- We specifically looked at scenarios where the percentage of the high-risk population using various prophylaxis options is held constant. We do include the possibility that there may be medically required PrEP medication discontinuation.
- Some of those within the AIDS compartment receive ART and may still transmit HIV.
- We exclude the cost of PrEP and the associated ancillary support services from the model since we are accessing data exclusive to the United States. As of July 2021, the Affordable Care Act requires all non-grandfathered in private health plans to cover the associated costs without cost sharing [16]. We acknowledge that other countries do not have this requirement and that this may thus affect PrEP access.

#### 2.1. The SIA Model

#### 2.2. The SPCBIA Model

_{p}cases can decrease through natural death ($\mu )$, death through HIV $\left(\nu \right)$, or can be transferred to another category $\left(\gamma \right)$, i.e., the development of AIDS. Similarly, an increase in the number of I

_{p}cases is proportional to the susceptible population using PrEP, (P), with the proportionality constant including terms involving the number of partners per year (r), the probability of transmission $\beta $, the probability of meeting an infected partner $({I}_{tot}+\eta A)/N$, and an estimation of PrEP effectiveness (1 − k).

## 3. Results

#### 3.1. Determination of Parameters

- (1)
- We calculate long-term populations and outcomes under an optimistic scenario defined as the complete proper usage of PrEP. This scenario utilizes different values of initial PrEP usage and identifies what values of PrEP usage may provide substantial improvements. Our optimistic values are 90% PrEP effectiveness, 91% condom effectiveness, and 99% effectiveness for those using both PrEP and condoms.
- (2)
- We examine the outcomes of a pessimistic scenario utilizing a low level of PrEP effectiveness by assuming that PrEP protocol adherence is wholly inconsistent and that there is a possibility of intravenous drug use. The pessimistic model uses 50% PrEP effectiveness, 64% condom effectiveness, and 82% effectiveness for those using both PrEP and condoms.
- (3)
- We explore the impact of how the average number of sexual partners per year affects the projection outcomes by comparing the results for two and four average sexual partners per year.
- (4)
- We look at a 50-year benchmark for various starting percentages of those using PrEP to explore outcomes as a function of PrEP usage.

#### 3.2. Optimistic Scenario Results

#### 3.3. Pessimistic Scenario Results

#### 3.4. 50-Year Benchmark

#### 3.5. Condom versus PrEP Usage

## 4. Discussion

## 5. Conclusions and Policy Implications

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**CDC data and SIA model projections for the susceptible, S(t); infected, I(t); and AIDS, A(t), populations as a function of time. The dashed lines are the recorded values from the CDC while the solid lines are the results of our SIA model.

**Figure 2.**The values for $\gamma $, $\nu $, and ${\nu}_{a}$ from the CDC data from 2008 to 2018. Note: 2012 is when PrEP was approved for use by the FDA [4].

**Figure 3.**The optimistic scenario implies strict adherence to proper PrEP usage. These graphs show the total susceptible (black line) and infected (red line) percentages as a function of time. In addition, the breakdown into the detailed makeup of each category is presented with the legend as shown in (

**b**), where ${S}_{tot}$ is the total number of susceptibles, ${I}_{tot}$ is the total infected, ${I}_{S}$ is the portion of ${I}_{tot}$ using no prophylaxis, ${I}_{P}$ is the portion of ${I}_{tot}$ using only PrEP, ${I}_{C}$ is the portion of ${I}_{tot}$ using only condoms, and ${I}_{B}$ is the portion of ${I}_{tot}$ using both PrEP and condoms. (

**a**) Projection when 10% of the population is using PrEP and the average number of sexual partners is two. (

**b**) Projection when 10% of the population is using PrEP and the average number of sexual partners is four. (

**c**) Projection when 70% of the population is using PrEP and the average number of sexual partners is two. (

**d**) Projection when 70% of the population is using PrEP and the average number of sexual partners is four.

**Figure 4.**The pessimistic scenario implies inconsistent PrEP usage. These graphs show the total susceptible (black line) and infected (red line) percentages as a function of time. In addition, the breakdown into the detailed makeup of each category is presented with the legend as shown in (

**b**), where ${S}_{tot}$ is the total number of susceptibles, ${I}_{tot}$ is the total infected, ${I}_{S}$ is the portion of ${I}_{tot}$ using no prophylaxis, is the portion of ${I}_{tot}$ using only PrEP, ${I}_{C}$ is the portion of ${I}_{tot}$ using only condoms, and ${I}_{B}$ is the portion of ${I}_{tot}$ using both PrEP and condoms. (

**a**) Projection when 10% of the population is using PrEP and the average number of sexual partners is two. (

**b**) Projection when 10% of the population is using PrEP and the average number of sexual partners is four. (

**c**) Projection when 70% of the population is using PrEP and the average number of sexual partners is two. (

**d**) Projection when 70% of the population is using PrEP and the average number of sexual partners is four.

**Figure 5.**This plot shows total susceptible and total infected population percentages as a function of PrEP usage at the 50-year mark for the optimistic (black and red) and the pessimistic (green and blue) scenarios. This uses the assumption of two partners/year.

Year | Susceptibles | Infected | AIDS | N ^{b} | Susceptibles/N | Infected/N | AIDS/N |
---|---|---|---|---|---|---|---|

2008 | 3,917,413 | 538,516 | 311,817 | 4,767,746 | 0.82207 | 0.11295 | 0.065401 |

2009 | 3,937,002 | 556,262 | 320,702 | 4,813,966 | 0.818247 | 0.115552 | 0.066619 |

2010 | 3,952,700 | 575,801 | 328,546 | 4,857,047 | 0.814221 | 0.11855 | 0.067643 |

2011 | 3,973,413 | 593,774 | 335,292 | 4,902,479 | 0.810901 | 0.121117 | 0.068392 |

2012 | 3,995,338 | 612,928 | 342,363 | 4,950,629 | 0.807443 | 0.123808 | 0.069155 |

2013 | 4,017,589 | 630,660 | 348,925 | 4,997,174 | 0.804375 | 0.126203 | 0.069824 |

2014 | 4,043,226 | 650,714 | 349,891 | 5,043,831 | 0.802017 | 0.129012 | 0.06937 |

2015 | 4,066,157 | 670,052 | 353,147 | 5,089,356 | 0.799349 | 0.131658 | 0.069389 |

2016 | 4,088,924 | 688,579 | 356,601 | 5,134,104 | 0.796817 | 0.134119 | 0.06457 |

2017 | 4,110,186 | 706,439 | 359,520 | 5,176,145 | 0.794453 | 0.13648 | 0.06457 |

2018 | 4,132,070 | 723,948 | 362,516 | 5,218,534 | 0.792193 | 0.138726 | 0.06467 |

^{a}The data are adapted from the anonymous and publicly accessible 2008 to 2018 CDC case surveillance data, which includes all 50 states, the District of Columbia, American Samoa, Guam, the Northern Mariana Islands, Puerto Rico, and the U.S. Virgin Islands [11].

^{b}N is the sum of the susceptibles, infected, and AIDS values representing the total population under consideration.

Parameter | Description | Value |
---|---|---|

$N\left(0\right)$ | Initial total high-risk population. | $4,767,746\mathrm{people}$^{b} |

$I\left(0\right)$ | Initial total infected. | $538,516\mathrm{people}$^{b} |

$A\left(0\right)$ | Initial total HIV stage III (AIDS) population. | $311,817\mathrm{people}$^{b} |

$S\left(0\right)$ | Initial susceptible population. | $N\left(0\right)-I\left(0\right)-A\left(0\right)$ |

$G$ | Recruitment rate. | $67,000/\mathrm{year}$ |

$r$ | Average number of sexual partners per year. | $2$ |

$\beta $ | Transmissions per partner. | $0.047$ |

$\eta $ | Modification parameter for relative AIDS infectiousness. | $1.235$ |

$\mu $ | Natural death rate. | $0.033/\mathrm{year}$ |

$\nu $ | HIV-related death rate. | $0.015557/\mathrm{year}$ |

${\nu}_{a}$ | AIDS-related death rate. | $0.023924/\mathrm{year}$ |

$\gamma $ | Rate of leaving high-risk population into AIDS. | $0.016960/\mathrm{year}$ |

$\alpha $ | A into treatment and able to transmit HIV. | $0.0045/\mathrm{year}$ |

^{a}All the rate parameters are for the normalized populations.

^{b}The population data are from the CDC case surveillance data for 2008.

Parameter | Description | Value |
---|---|---|

$N\left(0\right)$ | Initial total high-risk population. | $5,176,145\mathrm{people}$^{b} |

$I\left(0\right)$ | Initial total infected. | $706,439\mathrm{people}$^{b} |

$A\left(0\right)$ | Initial total HIV stage III (AIDS) population. | $359,520\mathrm{people}$^{b} |

$P\left(0\right)$ | Initial PrEP users. | Variable |

$C\left(0\right)$ | Initial condom users. | Variable |

$B\left(0\right)$ | Initial PrEP users using condoms. | Variable |

${S}_{tot}\left(0\right)$ | Total initial susceptible population. | $N\left(0\right)-I\left(0\right)-A\left(0\right)$ |

$S\left(0\right)$ | Initial susceptible population. | ${S}_{tot}\left(0\right)-P\left(0\right)-C\left(0\right)-B\left(0\right)$ |

${P}_{o}$ | Initial percentage of PrEP users. | Variable |

$\theta $ | $\mathrm{PrEP}$. | $0.001/\mathrm{year}$ |

$\xi $ | $\mathrm{Condom}$. | $0.01/\mathrm{year}$ |

$\omega $ | $\mathrm{PrEP}$. | $0.01/\mathrm{year}$ |

$\psi $ | $\mathrm{Percentage}\mathrm{of}{S}_{tot}$$\mathrm{in}$. | $\mathrm{Variable}$ |

$\delta $ | $\mathrm{Percentage}\mathrm{of}{S}_{tot}$$\mathrm{in}$. | $35\%$ |

$\chi $ | $\mathrm{Percentage}$$\mathrm{in}$. | $19\%$ |

^{a}All the rate parameters are for the normalized populations.

^{b}The population data are from the CDC case surveillance data for 2017.

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**MDPI and ACS Style**

Lewis, J.; Camley, R.E.
Exploring Projections for HIV Infection with Pre-Exposure Prophylaxis Usage in a High-Risk Population. *Appl. Sci.* **2022**, *12*, 8359.
https://doi.org/10.3390/app12168359

**AMA Style**

Lewis J, Camley RE.
Exploring Projections for HIV Infection with Pre-Exposure Prophylaxis Usage in a High-Risk Population. *Applied Sciences*. 2022; 12(16):8359.
https://doi.org/10.3390/app12168359

**Chicago/Turabian Style**

Lewis, Jeramy, and Robert E. Camley.
2022. "Exploring Projections for HIV Infection with Pre-Exposure Prophylaxis Usage in a High-Risk Population" *Applied Sciences* 12, no. 16: 8359.
https://doi.org/10.3390/app12168359