A mathematical model for HIV and hepatitis C co-infection and its assessment from a statistical perspective

Mathematical modeling of HIV-HCV co-infection model: Impact of parameters on reproduction number

Background: Hepatitis C Virus (HCV) and Human Immunodeficiency Virus (HIV) are both as classified blood-borne viruses since they are transmitted through contact with contaminated blood. Approximately 1.3 million of the 2.75 million global HIV/HCV carriers inject drugs (PWID). HIV co-infection has a harmful effect on the progression of HCV, resulting in greater rates of HCV persistence after acute infection, higher viral levels, and accelerated progression of liver fibrosis and end-stage liver disease. In this study, we developed and investigated a mathematical model for the dynamical behavior of HIV/AIDS and HCV co-infection, which includes therapy for both diseases, vertical transmission in HIV cases, unawareness and awareness of HIV infection, inefficient HIV treatment follow-up, and efficient condom use. Methods: Positivity and boundedness of the model under investigation were established using well-known theorems. The equilibria were demonstrated by bringing all differential equations to zero. The associative reproduction numbers for mono-infected and dual-infected models were calculated using the next-generation matrix approach. The local and global stabilities of the models were validated using the linearization and comparison theorem and the negative criterion techniques of bendixson and dulac, respectively. Results: The growing prevalence of HIV treatment dropout in each compartment of the HIV model led to a reduction in HIV on treatment compartments while other compartments exhibited an increase in populations . In dually infected patients, treating HCV first reduces co-infection reproduction number R ech , which reduces liver cancer risk. Conclusions: From the model's results, we infer various steps that policymakers could take to reduce the number of mono-infected and co-infected individuals.

Mathematical modeling of HIV-HCV co-infection model: Impact of parameters on reproduction number

Background: Hepatitis C Virus (HCV) and Human Immunodeficiency Virus (HIV) are both classified as blood-borne viruses since they are transmitted through contact with contaminated blood. Approximately 1.3 million of the 2.75 million global HIV/HCV carriers are people who inject drugs (PWID). HIV co-infection has a harmful effect on the progression of HCV, resulting in greater rates of HCV persistence after acute infection, higher viral levels, and accelerated progression of liver fibrosis and end-stage liver disease. In this study, we developed and investigated a mathematical model for the dynamical behavior of HIV/AIDS and HCV co-infection, which includes therapy for both diseases, vertical transmission in HIV cases, unawareness and awareness of HIV infection, inefficient HIV treatment follow-up, and efficient condom use. Methods: Positivity and boundedness of the model under investigation were established using well-known theorems. The equilibria were demonstrated by bringing all differential equations to zero. The associative reproduction numbers for mono-infected and dual-infected models were calculated using the next-generation matrix approach. The local and global stabilities of the models were validated using the linearization and comparison theorem and the negative criterion techniques of bendixson and dulac, respectively. Results: The growing prevalence of HIV treatment dropout in each compartment of the HIV model led to a reduction in HIV on treatment compartments while other compartments exhibited an increase in populations . In dually infected patients, treating HCV first reduces co-infection reproduction number R ech , which reduces liver cancer risk. Conclusions: From the model's results, we infer various steps (such as: campaigns to warn individuals about the consequences of having multiple sexual partners; distributing more condoms to individuals; continuing treatment for chronic HCV and AIDS) that policymakers could take to reduce the number of mono-infected and co-infected individuals.

Influence of sexual risk behaviour and STI co-infection dynamics on the evolution of HIV set point viral load in MSM

HIV viral load (VL) is an important predictor of HIV progression and transmission. Anti-retroviral therapy (ART) has been reported to reduce HIV transmission by lowering VL. However, apart from this beneficial effect, increased levels of population mean set-point viral load (SPVL), an estimator for HIV virulence, have been observed in men who have sex with men (MSM) in the decade following the introduction of ART in The Netherlands. Several studies have been devoted to explain these counter-intuitive trends in SPVL. However, to our knowledge, none of these studies has investigated an explanation in which it arises as the result of a sexually transmitted infection (STI) co-factor in detail. In this study, we adapted an event-based, individual-based model to investigate how STI co-infection and sexual risk behaviour affect the evolution of HIV SPVL in MSM before and after the introduction of ART. The results suggest that sexual risk behaviour has an effect on SPVL and indicate that more data are needed to test the effect of STI co-factors on SPVL. Furthermore, the observed trends in SPVL cannot be explained by sexual risk behaviour and STI co-factors only. We recommend to develop mathematical models including also factors related to viral evolution as reported earlier in the literature. However, this requires more complex models, and the collection of more data for parameter estimation than what is currently available.

The transmissibility of hepatitis C virus: a modelling study in Xiamen City, China

This study aimed at estimating the transmissibility of hepatitis C. The data for hepatitis C cases were collected in six districts in Xiamen City, China from 2004 to 2018. A population-mixed susceptible-infectious-chronic-recovered (SICR) model was used to fit the data and the parameters of the model were calculated. The basic reproduction number (R0) and the number of newly transmitted cases by a primary case per month (MNI) were adopted to quantitatively assess the transmissibility of hepatitis C virus (HCV). Eleven curve estimation models were employed to predict the trends of R0 and MNI in the city. The SICR model fits the reported HCV data well (P < 0.01). The median R0 of each district in Xiamen is 0.4059. R0 follows the cubic model curve, the compound curve and the power function curve. The median MNI of each district in Xiamen is 0.0020. MNI follows the cubic model curve, the compound curve and the power function curve. The transmissibility of HCV follows a decreasing trend, which reveals that under the current policy for prevention and control, there would be a high feasibility to eliminate the transmission of HCV in the city.

Mathematical Modelling of HIV-HCV Coinfection Dynamics in Absence of Therapy

Globally, it is estimated that of the 36.7 million people infected with human immunodeficiency virus (HIV), 6.3% are coinfected with hepatitis C virus (HCV). Coinfection with HIV reduces the chance of HCV spontaneous clearance. In this work, we formulated and analysed a deterministic model to study the HIV and HCV coinfection dynamics in absence of therapy. Due to chronic stage of HCV infection being long, asymptomatic, and infectious, our model formulation was based on the splitting of the chronic stage into the following: before onset of cirrhosis and its complications and after onset of cirrhosis. We computed the basic reproduction numbers using the next generation matrix method. We performed numerical simulations to support the analytical results. We carried out sensitivity analysis to determine the relative importance of the different parameters influencing the HIV-HCV coinfection dynamics. The findings reveal that, in the long run, there is a substantial number of individuals coinfected with HIV and latent HCV. Therefore, HIV and latently HCV-infected individuals need to seek early treatment so as to slow down the progression of HIV to AIDS and latent HCV to advanced HCV.

Mathematical modeling of hepatitis c virus (HCV) prevention among people who inject drugs: A review of the literature and insights for elimination strategies

In 2016, the World Health Organization issued global elimination targets for hepatitis C virus (HCV), including an 80% reduction in HCV incidence by 2030. The vast majority of new HCV infections occur among people who inject drugs (PWID), and as such elimination strategies require particular focus on this population. As governments urgently require guidance on how to achieve elimination among PWID, mathematical modeling can provide critical information on the level and targeting of intervention are required. In this paper we review the epidemic modeling literature on HCV transmission and prevention among PWID, highlight main differences in mathematical formulation, and discuss key insights provided by these models in terms of achieving WHO elimination targets among PWID. Overall, the vast majority of modeling studies utilized a deterministic compartmental susceptible-infected-susceptible structure, with select studies utilizing individual-based network transmission models. In general, these studies found that harm reduction alone is unlikely to achieve elimination targets among PWID. However, modeling indicates elimination is achievable in a wide variety of epidemic settings with harm reduction scale-up combined with modest levels of HCV treatment for PWID. Unfortunately, current levels of testing and treatment are generally insufficient to achieve elimination in most settings, and require further scale-up. Additionally, network-based treatment strategies as well as prison-based treatment and harm reduction provision could provide important additional population benefits. Overall, epidemic modeling has and continues to play a critical role in informing HCV elimination strategies worldwide.

Age- and time-dependent prevalence and incidence of hepatitis C virus infection in drug users in France, 2004-2011: model-based estimation from two national cross-sectional serosurveys

Hepatitis C virus (HCV) infection is a public health issue worldwide. Injecting drug use remains the major mode of transmission in developed countries. Monitoring the HCV transmission dynamic over time is crucial, especially to assess the effect of harm reduction measures in drug users (DU). Our objective was to estimate the prevalence and incidence of HCV infection in DU in France using data from a repeated cross-sectional survey conducted in 2004 and 2011. Age- and time-dependent HCV prevalence was estimated through logistic regression models adjusted for HIV serostatus or injecting practices. HCV incidence was estimated from a mathematical model linking prevalence and incidence. HCV prevalence decreased from 58·2% [95% confidence interval (CI) 49·7-66·8] in 2004 to 43·2% (95% CI 38·8-47·7) in 2011. HCV incidence decreased from 7·9/100 person-years (95% CI 6·4-9·4) in 2004 to 4·4/100 person-years (95% CI 3·3-5·9) in 2011. HCV prevalence and incidence were significantly associated with age, calendar time, HIV serostatus and injecting practices. In 2011, the highest estimated incidence was in active injecting DU (11·2/100 person-years). Given the forthcoming objective of generalizing access to new direct antiviral agents for HCV infection, our results contribute to decision-making and policy development regarding treatment scale-up and disease prevention in the DU population.

Integrating between-host transmission and within-host immunity to analyze the impact of varicella vaccination on zoster

Varicella-zoster virus (VZV) causes chickenpox and reactivation of latent VZV causes herpes zoster (HZ). VZV reactivation is subject to the opposing mechanisms of declining and boosted VZV-specific cellular mediated immunity (CMI). A reduction in exogenous re-exposure ‘opportunities’ through universal chickenpox vaccination could therefore lead to an increase in HZ incidence. We present the first individual-based model that integrates within-host data on VZV-CMI and between-host transmission data to simulate HZ incidence. This model allows estimating currently unknown pivotal biomedical parameters, including the duration of exogenous boosting at 2 years, with a peak threefold to fourfold increase of VZV-CMI; the VZV weekly reactivation probability at 5% and VZV subclinical reactivation having no effect on VZV-CMI. A 100% effective chickenpox vaccine given to 1 year olds would cause a 1.75 times peak increase in HZ 31 years after implementation. This increase is predicted to occur mainly in younger age groups than is currently assumed.

DOI:http://dx.doi.org/10.7554/eLife.07116.001

The itchy-scratchy misery of a chickenpox was until recently a rite of passage for children around the world. The varicella-zoster virus causes chickenpox infections. This virus persists in small numbers in nerve cells for many years after infection, and can reactivate from these cells. Often this reactivation causes no symptoms, but sometimes it results in a painful skin condition called shingles (or herpes zoster), especially in older adults.

Some countries—including the United States, Australia, Taiwan and Greece—have virtually wiped out childhood cases of chickenpox by requiring that children be vaccinated against the varicella-zoster virus. But some countries have hesitated. One reason for this hesitation is that exposure to individuals with a chickenpox infection helps boost the immunity of individuals who have previously been infected. This may help reduce the likelihood of these people developing shingles later in life. So, some countries have worried that chickenpox vaccinations might inadvertently increase the number of shingles cases. To assess this risk, many scientists have created computer models, but the models have some limitations.

Now, Ogunjimi et al. report a new individual-based model to assess the effect of childhood varicella vaccination on shingles cases that factors in the immune responses to varicella infection. The model suggests that re-exposure to the varicella virus through contact with infected people would only provide extra protection for about two years; this is much shorter than previous predictions that suggested it might last 20 years. The model also predicts that implementing a varicella vaccination program for children would almost double the number of shingles cases 31 years later. But this increase would be temporary.

The predicted increase in shingles cases is likely to disproportionately occur among 31- to 40-year-olds. This is unexpected because most previous models predict that older age groups would bear the brunt of a rise in shingles, but this younger population would be less likely to develop lasting complications of shingles. Together, these findings may allay some fears about implementing childhood varicella vaccination programs by showing that the benefits of re-exposure are limited.

DOI:http://dx.doi.org/10.7554/eLife.07116.002

Dynamic modelling of hepatitis C virus transmission among people who inject drugs: a methodological review

Equipment sharing among people who inject drugs (PWID) is a key risk factor in infection by hepatitis C virus (HCV). Both the effectiveness and cost-effectiveness of interventions aimed at reducing HCV transmission in this population (such as opioid substitution therapy, needle exchange programmes or improved treatment) are difficult to evaluate using field surveys. Ethical issues and complicated access to the PWID population make it difficult to gather epidemiological data. In this context, mathematical modelling of HCV transmission is a useful alternative for comparing the cost and effectiveness of various interventions. Several models have been developed in the past few years. They are often based on strong hypotheses concerning the population structure. This review presents compartmental and individual-based models to underline their strengths and limits in the context of HCV infection among PWID. The final section discusses the main results of the papers.

Modelling in concentrated epidemics: informing epidemic trajectories and assessing prevention approaches

PURPOSE OF THE REVIEW

This review summarizes recent mathematical modelling studies conducted among key populations including MSM, people who inject drugs (PWID), and female sex workers (FSWs) in low prevalence settings used as a marker of concentrated epidemics.

RECENT FINDINGS

Most recent studies focused on MSM, Asian settings or high-income countries, studied the transmission dynamics or modelled pre-exposure prophylaxis, treatment as prevention or behavioural interventions specific to each key population (e.g., needle exchange programme or use of low-dead space syringes for PWID). Biological interventions were deemed effective and cost-effective, though still expensive, and often deemed unlikely to result in HIV elimination if used alone. Targeting high-risk individuals even within key populations improved efficiency. Some studies made innovative use of models to formally evaluate HIV prevention programmes, to interpret genetic or co-infection data, and to address methodological questions and validate epidemiological tools.

CONCLUSION

More work is needed to optimize combination prevention focusing on key populations in different settings. The gaps identified include the limited number of studies modelling drug resistance, structural interventions, treatment as prevention among FSWs, and estimating the contribution of key populations to overall transmission in different settings.

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.

Vertical transmission of hepatitis C virus: systematic review and meta-analysis

Updated pooled estimates of vertical hepatitis C (HCV) infection risk to children of HCV RNA–positive mothers ranges between 5.8% and 10.8%, depending on maternal HIV coinfection. Additional risk factors need to be captured and reported by future studies.

Background. We conducted a systematic review of estimates of hepatitis C virus (HCV) vertical transmission risk to update current estimates published more than a decade ago.

Methods. PubMed and Embase were searched and 109 articles were included. Pooled estimates of risk were generated for children born to HCV antibody–positive and viremic women, aged ≥18 months, separately by maternal human immunodeficiency virus (HIV) coinfection.

Results. Meta-analysis of the risk of vertical HCV infection to children of HCV antibody–positive and RNA-positive women was 5.8% (95% confidence interval [CI], 4.2%–7.8%) for children of HIV-negative women and 10.8% (95% CI, 7.6%–15.2%) for children of HIV-positive women. The adjusted meta-regression model explained 51% of the between-study variation in the 25 included risk estimates. Maternal HIV coinfection was the most important determinant of vertical transmission risk (adjusted odds ratio, 2.56 [95% CI, 1.50–4.43]). Additional methodological (follow-up rate and definition of infection in children) and risk factors independently predicted HCV infection and need to be captured and reported by future studies of vertical transmission. Studies assessing the contribution of nonvertical exposures in early childhood to HCV prevalence among children at risk of vertical transmission are needed.

Conclusions. More than 1 in every 20 children delivered by HCV chronically infected women are infected, highlighting that vertical transmission likely constitutes the primary transmission route among children. These updated estimates are a basis for decision making in prioritization of research into risk-reducing measures, and inform case management in clinical settings, especially for HIV-positive women in reproductive age.

Two decades of successes and failures in controlling the transmission of HIV through injecting drug use in England and Wales, 1990 to 2011

Responses to injecting drug use have changed focus over the last 20 years. Prevalence and incidence of human immunodeficiency virus (HIV) among people who inject drugs (PWID) in England and Wales were examined in relation to these changes. A voluntary unlinked-anonymous surveillance study obtained a biological sample and questionnaire data from PWID through annual surveys since 1990. Prevalence and incidence trends were estimated via generalised linear models, and compared with a policy time-line. Overall HIV prevalence among 38,539 participations was 1.15%. Prevalence was highest among those who started injecting before 1985; throughout the 1990s, prevalence fell in this group and was stable among those who started injecting later. Prevalence was higher in 2005 than 2000 (odds ratio: 3.56 (95% confidence interval (CI) 1.40–9.03) in London, 3.40 (95% CI 2.31–5.02) elsewhere). Estimated HIV incidence peaked twice, around 1983 and 2005. HIV was an important focus of policy concerning PWID from 1984 until 1998. This focus shifted at a time when drug use and risk were changing. The increased incidence in 2005 cannot be ascribed to the policy changes, but these appeared to be temporally aligned. Policy related to PWID should be continually reviewed to ensure rapid responses to increased risk.