Modelling HIV/AIDS in the presence of an HIV testing and screening campaign

Understanding HIV/AIDS dynamics: insights from CD4+T cells, antiretroviral treatment, and country-specific analysis

In this article, we present a mathematical model for human immunodeficiency virus (HIV)/Acquired immune deficiency syndrome (AIDS), taking into account the number of CD4+T cells and antiretroviral treatment. This model is developed based on the susceptible, infected, treated, AIDS (SITA) framework, wherein the infected and treated compartments are divided based on the number of CD4+T cells. Additionally, we consider the possibility of treatment failure, which can exacerbate the condition of the treated individual. Initially, we analyze a simplified HIV/AIDS model without differentiation between the infected and treated classes. Our findings reveal that the global stability of the HIV/AIDS-free equilibrium point is contingent upon the basic reproduction number being less than one. Furthermore, a bifurcation analysis demonstrates that our simplified model consistently exhibits a transcritical bifurcation at a reproduction number equal to one. In the complete model, we elucidate how the control reproduction number determines the stability of the HIV/AIDS-free equilibrium point. To align our model with the empirical data, we estimate its parameters using prevalence data from the top four countries affected by HIV/AIDS, namely, Eswatini, Lesotho, Botswana, and South Africa. We employ numerical simulations and conduct elasticity and sensitivity analyses to examine how our model parameters influence the control reproduction number and the dynamics of each model compartment. Our findings reveal that each country displays distinct sensitivities to the model parameters, implying the need for tailored strategies depending on the target country. Autonomous simulations highlight the potential of case detection and condom use in reducing HIV/AIDS prevalence. Furthermore, we identify that the quality of condoms plays a crucial role: with higher quality condoms, a smaller proportion of infected individuals need to use them for the potential eradication of HIV/AIDS from the population. In our optimal control simulations, we assess population behavior when control interventions are treated as time-dependent variables. Our analysis demonstrates that a combination of condom use and case detection, as time-dependent variables, can significantly curtail the spread of HIV while maintaining an optimal cost of intervention. Moreover, our cost-effectiveness analysis indicates that the condom use intervention alone emerges as the most cost-effective strategy, followed by a combination of case detection and condom use, and finally, case detection as a standalone strategy.

Impact of voluntary testing on infectious disease epidemiology: A game theoretic approach

The World Health Organization recommends test-and-treat interventions to curb and even eliminate epidemics of HIV, viral hepatitis, and sexually transmitted infections (e.g., chlamydia, gonorrhea, syphilis and trichomoniasis). Epidemic models show these goals are achievable, provided the participation of individuals in test-and-treat interventions is sufficiently high. We combine epidemic models and game theoretic models to describe individual's decisions to get tested for infectious diseases within certain epidemiological contexts, and, implicitly, their voluntary participation to test-and-treat interventions. We develop three hybrid models, to discuss interventions against HIV, HCV, and sexually transmitted infections, and the potential behavioral response from the target population. Our findings are similar across diseases. Particularly, individuals use three distinct behavioral patterns relative to testing, based on their perceived costs for testing, besides the payoff for discovering their disease status. Firstly, if the cost of testing is too high, then individuals refrain from voluntary testing and get tested only if they are symptomatic. Secondly, if the cost is moderate, some individuals will test voluntarily, starting treatment if needed. Hence, the spread of the disease declines and the disease epidemiology is mitigated. Thirdly, the most beneficial testing behavior takes place as individuals perceive a per-test payoff that surpasses a certain threshold, every time they get tested. Consequently, individuals achieve high voluntary testing rates, which may result in the elimination of the epidemic, albeit on temporary basis. Trials and studies have attained different levels of participation and testing rates. To increase testing rates, they should provide each eligible individual with a payoff, above a given threshold, each time the individual tests voluntarily.

Transmission dynamics of a novel HIV/AIDS model through a higher-order Galerkin time discretization scheme

There are numerous contagious diseases caused by pathogenic microorganisms, including bacteria, viruses, fungi, and parasites, that have the propensity to culminate in fatal consequences. A communicable disease is an illness caused by a contagion agent or its toxins and spread directly or indirectly to a susceptible animal or human host by an infected person, animal, vector, or immaterial environment. Human immunodeficiency virus (HIV) infection, hepatitis A, B, and C, and measles are all examples of communicable diseases. Acquired immunodeficiency syndrome (AIDS) is a communicable disease caused by HIV infection that has become the most severe issue facing humanity. The research work in this paper is to numerically explore a mathematical model and demonstrate the dynamics of HIV/AIDS disease transmission using a continuous Galerkin-Petrov time discretization of a higher-order scheme, specifically the cGP(2)-scheme. Depict a graphical and tabular comparison between the outcomes of the mentioned scheme and those obtained through other classical schemes that exist in the literature. Further, a comparison is performed relative to the well-known fourth-order Ruge-Kutta (RK4) method with different step sizes. By contrast, the suggested approach provided more accurate results with a larger step size than RK4 with a smaller step size. After validation and confirmation of the suggested scheme and code, we implement the method to the extended model by introducing a treatment rate and show the impact of various non-linear source terms for the generation of new cells. We also determined the basic reproduction number and use the Routh-Hurwitz criterion to assess the stability of disease-free and unique endemic equilibrium states of the HIV model.

Modelling Botswana's HIV/AIDS response and treatment policy changes: Insights from a cascade of mathematical models

The management of HIV/AIDS has evolved ever since advent of the disease in the past three decades. Many countries have had to revise their policies as new information on the virus, and its transmission dynamics emerged. In this paper, we track the changes in Botswana's HIV/AIDS response and treatment policies using a piece-wise system of differential equations. The policy changes are easily tracked in three epochs. Models for each era are formulated from a "grand model" that can be linked to all the epochs. The grand model's steady states are determined and analysed in terms of the model reproduction number, $ R_{0}. $ The model exhibits a backward bifurcation, where a stable disease-free equilibrium coexists with a stable endemic equilibrium when $ R_{0} < 1. $ The stability of the models for the other epochs can be derived from that of the grand model by setting some parameters to zero. The models are fitted to HIV/AIDS prevalence data from Botswana for the past three decades. The changes in the populations in each compartment are tracked as the response to the disease and treatment policy changed over time. Finally, projections are made to determine the possible trajectory of HIV/AIDS in Botswana. The implications of the policy changes are easily seen, and a discussion on how these changes impacted the epidemic are articulated. The results presented have crucial impact on how policy changes affected and continue to influence the trajectory of the HIV/AIDS epidemic in Botswana.

Estimating the HIV Effective Reproduction Number in the United States and Evaluating HIV Elimination Strategies

CONTEXT

The reproduction number is a fundamental epidemiologic concept used to assess the potential spread of infectious diseases and whether they can be eliminated.

OBJECTIVE

We estimated the 2017 United States HIV effective reproduction number, Re, the average number of secondary infections from an infected person in a partially infected population. We analyzed the potential effects on Re of interventions aimed at improving patient flow rates along different stages of the HIV care continuum. We also examined these effects by individual transmission groups.

DESIGN

We used the HIV Optimization and Prevention Economics (HOPE) model, a compartmental model of disease progression and transmission, and the next-generation matrix method to estimate Re. We then projected the impact of changes in HIV continuum-of-care interventions on the continuum-of-care flow rates and the estimated Re in 2020.

SETTING

United States.

PARTICIPANTS

The HOPE model simulated the sexually active US population and persons who inject drugs, aged 13 to 64 years, which was stratified into 195 subpopulations by transmission group, sex, race/ethnicity, age, male circumcision status, and HIV risk level.

MAIN OUTCOME MEASURES

The estimated value of Re in 2017 and changes in Re in 2020 from interventions affecting the continuum-of-care flow rates.

RESULTS

Our estimated HIV Re in 2017 was 0.92 [0.82, 0.94] (base case [min, max across calibration sets]). Among the interventions considered, the most effective way to reduce Re substantially below 1.0 in 2020 was to maintain viral suppression among those receiving HIV treatment. The greatest impact on Re resulted from changing the flow rates for men who have sex with men (MSM).

CONCLUSIONS

Our results suggest that current prevention and treatment efforts may not be sufficient to move the country toward HIV elimination. Reducing Re to substantially below 1.0 may be achieved by an ongoing focus on early diagnosis, linkage to care, and sustained viral suppression especially for MSM.

Perceptions of cervical cancer and motivation for screening among women in Rural Lilongwe, Malawi: A qualitative study

INTRODUCTION

Cervical cancer is the leading cause of cancer death among women in Malawi. Low awareness of cervical cancer and negative perceptions of screening can prevent women from participating in preventative strategies. We sought to explore perceptions and motivations for screening among women who participated in a cervical cancer screen-and-treat pilot study in rural Malawi.

MATERIALS AND METHODS

We conducted a qualitative sub-study of a community-based cervical cancer screen-and-treat pilot study in rural Lilongwe between July-August 2017. From October 2017-February 2018, 17 women who underwent screening using visual inspection with acetic acid (VIA) and same-day thermal ablation treatment were recruited at their 12-week follow-up visit post treatment to participate in this qualitative sub-study. Semi-structured interview guides that explored baseline knowledge of cervical cancer, perceptions, and motivation for screening were used for in-depth interviews (IDIs). IDIs were conducted in the local language, Chichewa, translated and transcribed to English. Data was analyzed using NVivo® V12.0.

RESULTS

Findings included fatalistic views on cancer, but limited knowledge specific to cervical cancer. Misconceptions of cervical cancer screening were common; however, there was a unique understanding of screening as prevention (i.e., finding and treating early disease to prevent progression to worsening disease). This understanding appeared to stem from HIV prevention concepts known to the community. Motivations for screening included desire to know one's health status, convenience of community-based screening, and peer encouragement.

CONCLUSION

Despite limited knowledge of cervical cancer and misconceptions of screening, the concept of screening for prevention, desire to know one's health status, convenient access, and peers' influence were motivators for participation in screening. Cervical cancer screen-and-treat programs in high HIV prevalence areas should consider utilizing language that parallels HIV prevention language to communicate the need for cervical cancer screening and treatment and utilize prevention concepts that may already be familiar to women living there.

Analysing the impact of migration on HIV/AIDS cases using epidemiological modelling to guide policy makers

In this paper, we present the impact of migration on the spread of HIV and AIDS cases. A simple model for HIV and AIDS that incorporates migration and addresses its contributions to the spread of HIV and AIDS cases was constructed. The model was calibrated to HIV and AIDS incidence data from Malaysia. We explore the use of Markov chain Monte Carlo (MCMC) simulation method to estimate uncertainty in all the unknown parameters incorporated in our proposed model. Among the migrant population, 1.5572e-01 were susceptible to HIV transmission, which constituted 67,801 migrants. A proportion of migrants, 6.3773e-04, were estimated to be HIV infected, constituting 278 migrants. There were 72 (per 10,000) migrants estimated to have had AIDS, representing a proportion of 1.6611e-08. The result suggests that the disease-free steady state was unstable since the estimated basic reproduction number R0 was 2.0906 and 2.3322 for the models without and with migration, respectively. This is not a good indicator from the public health point of view, as the aim is to stabilize the epidemic at the disease-free equilibrium. The advantage of introduction of migration to the simple model validated the true R0 and the transmission rate β associated with HIV and AIDS epidemic disease in Malaysia. It also indicates an approximately 12 percentage points increase in the rate of HIV infection with migration.

The impact of implementing HIV prevention policies therapy and control strategy among HIV and AIDS incidence cases in Malaysia

Malaysia is faced with a high HIV/AIDS burden that poses a public health threat. We constructed and applied a compartmental model to understand the spread and control of HIV/AIDS in Malaysia. A simple model for HIV and AIDS disease that incorporates condom and uncontaminated needle-syringes interventions and addresses the relative impact of given treatment therapy for infected HIV newborns on reducing HIV and AIDS incidence is presented. We demonstrated how treatment therapy for new-born babies and the use of condoms or uncontaminated needle-syringes impact the dynamics of HIV in Malaysia. The model was calibrated to HIV and AIDS incidence data from Malaysia from 1986 to 2011. The epidemiological parameters are estimated using Bayesian inference via Markov chain Monte Carlo simulation method. The reproduction number optimal for control of the HIV/AIDS disease obtained suggests that the disease-free equilibrium was unstable during the 25 years. However, the results indicated that the use of condoms and uncontaminated needle-syringes are pivotal intervention control strategies; a comprehensive adoption of the intervention may help stop the spread of HIV disease. Treatment therapy for newborn babies is also of high value; it reduces the epidemic peak. The combined effect of condom use or uncontaminated needle-syringe is more pronounced in controlling the spread of HIV/AIDS.

Impact of early treatment programs on HIV epidemics: An immunity-based mathematical model

While studies on pre-exposure prophylaxis (PrEP) and post-exposure prophylaxis (PEP) have demonstrated substantial advantages in controlling HIV transmission, the overall benefits of the programs with early initiation of antiretroviral therapy (ART) have not been fully understood and are still on debate. Here, we develop an immunity-based (CD4+ T cell count based) mathematical model to study the impacts of early treatment programs on HIV epidemics and the overall community-level immunity. The model is parametrized using the HIV prevalence data from South Africa and fully analyzed for stability of equilibria and infection persistence criteria. Using our model, we evaluate the effects of early treatment on the new infection transmission, disease death, basic reproduction number, HIV prevalence, and the community-level immunity. Our model predicts that the programs with early treatments significantly reduce the new infection transmission and increase the community-level immunity, but the treatments alone may not be enough to eliminate HIV epidemics. These findings, including the community-level immunity, might provide helpful information for proper implementation of HIV treatment programs.

EFFECTS OF TREATMENT, AWARENESS AND CONDOM USE IN A COINFECTION MODEL FOR HIV AND HCV IN MSM

We develop a new a coinfection model for hepatitis C virus (HCV) and the human immunodeficiency virus (HIV). We consider treatment for both diseases, screening, unawareness and awareness of HIV infection, and the use of condoms. We study the local stability of the disease-free equilibria for the full model and for the two submodels (HCV only and HIV only submodels). We sketch bifurcation diagrams for different parameters, such as the probabilities that a contact will result in a HIV or an HCV infection. We present numerical simulations of the full model where the HIV, HCV and double endemic equilibria can be observed. We also show numerically the qualitative changes of the dynamical behavior of the full model for variation of relevant parameters. We extrapolate the results from the model for actual measures that could be implemented in order to reduce the number of infected individuals.

An Epidemic Patchy Model with Entry-Exit Screening

A multi-patch SEIQR epidemic model is formulated to investigate the long-term impact of entry-exit screening measures on the spread and control of infectious diseases. A threshold dynamics determined by the basic reproduction number R₀ is established: The disease can be eradicated if R₀ < 1, while the disease persists if R₀ > 1. As an application, six different screening strategies are explored to examine the impacts of screening on the control of the 2009 influenza A (H1N1) pandemic. We find that it is crucial to screen travelers from and to high-risk patches, and it is not necessary to implement screening in all connected patches, and both the dispersal rates and the successful detection rate of screening play an important role on determining an effective and practical screening strategy.

A coinfection model for HIV and HCV

We study a mathematical model for the human immunodeficiency virus (HIV) and hepatites C virus (HCV) coinfection. The model predicts four distinct equilibria: the disease free, the HIV endemic, the HCV endemic, and the full endemic equilibria. The local and global stability of the disease free equilibrium was calculated for the full model and the HIV and HCV submodels. We present numerical simulations of the full model where the distinct equilibria can be observed. We show simulations of the qualitative changes of the dynamical behavior of the full model for variation of relevant parameters. From the results of the model, we infer possible measures that could be implemented in order to reduce the number of infected individuals.