Conflict and accord of optimal treatment strategies for HIV infection within and between hosts

Optimal control of a multi-scale HIV-opioid model

In this study, we apply optimal control theory to an immuno-epidemiological model of HIV and opioid epidemics. For the multi-scale model, we used four controls: treating the opioid use, reducing HIV risk behaviour among opioid users, entry inhibiting antiviral therapy, and antiviral therapy which blocks the viral production. Two population-level controls are combined with two within-host-level controls. We prove the existence and uniqueness of an optimal control quadruple. Comparing the two population-level controls, we find that reducing the HIV risk of opioid users has a stronger impact on the population who is both HIV-infected and opioid-dependent than treating the opioid disorder. The within-host-level antiviral treatment has an effect not only on the co-affected population but also on the HIV-only infected population. Our findings suggest that the most effective strategy for managing the HIV and opioid epidemics is combining all controls at both within-host and between-host scales.

A mathematical model for HIV dynamics with multiple infections: implications for immune escape

Multiple infections enable the recombination of different strains, which may contribute to viral diversity. How multiple infections affect the competition dynamics between the two types of strains, the wild and the immune escape mutant, remains poorly understood. This study develops a novel mathematical model that includes the two strains, two modes of viral infection, and multiple infections. For the representative double-infection case, the reproductive numbers are derived and global stabilities of equilibria are obtained via the Lyapunov direct method and theory of limiting systems. Numerical simulations indicate similar viral dynamics regardless of multiplicities of infections though the competition between the two strains would be the fiercest in the case of quadruple infections. Through sensitivity analysis, we evaluate the effect of parameters on the set-point viral loads in the presence and absence of multiple infections. The model with multiple infections predict that there exists a threshold for cytotoxic T lymphocytes (CTLs) to minimize the overall viral load. Weak or strong CTLs immune response can result in high overall viral load. If the strength of CTLs maintains at an intermediate level, the fitness cost of the mutant is likely to have a significant impact on the evolutionary dynamics of mutant viruses. We further investigate how multiple infections alter the viral dynamics during the combination antiretroviral therapy (cART). The results show that viral loads may be underestimated during cART if multiple-infection is not taken into account.

Mathematical methods for scaling from within-host to population-scale in infectious disease systems

Mathematical modellers model infectious disease dynamics at different scales. Within-host models represent the spread of pathogens inside an individual, whilst between-host models track transmission between individuals. However, pathogen dynamics at one scale affect those at another. This has led to the development of multiscale models that connect within-host and between-host dynamics. In this article, we systematically review the literature on multiscale infectious disease modelling according to PRISMA guidelines, dividing previously published models into five categories governing their methodological approaches (Garira (2017)), explaining their benefits and limitations. We provide a primer on developing multiscale models of infectious diseases.

Modelling the impact of treatment adherence on the transmission of HIV drug resistance

INTRODUCTION

A lower adherence rate (percentage of individuals taking drugs as prescribed) to ART may increase the risk of emergence and transmission of HIV drug resistance, decrease treatment efficacy, and increase mortality rate. Exploring the impact of ART adherence on the transmission of drug resistance could provide insights in controlling the HIV epidemic.

METHODS

We proposed a dynamic transmission model incorporating the CD4 cell count-dependent rates of diagnosis, treatment and adherence with transmitted drug resistance (TDR) and acquired drug resistance. This model was calibrated and validated by 2008-2018 HIV/AIDS surveillance data and prevalence of TDR among newly diagnosed treatment-naive individuals from Guangxi, China, respectively. We aimed to identify the impact of adherence on drug resistance and deaths during expanding ART.

RESULTS

In the base case (ART at 90% adherence and 79% coverage), we projected the cumulative total new infections, new drug-resistant infections, and HIV-related deaths between 2022 and 2050 would be 420 539, 34 751 and 321 671. Increasing coverage to 95% would reduce the above total new infections (deaths) by 18.85% (15.75%). Reducing adherence to below 57.08% (40.84%) would offset these benefits of increasing coverage to 95% in reducing infections (deaths). Every 10% decrease in adherence would need 5.07% (3.62%) increase in coverage to avoid an increase in infections (deaths). Increasing coverage to 95% with 90% (80%) adherence would increase the above drug-resistant infections by 11.66% (32.98%).

CONCLUSIONS

A decrease in adherence might offset the benefits of ART expansion and exacerbate the transmission of drug resistance. Ensuring treated patients' adherence might be as important as expanding ART to untreated individuals.

The impact of attrition on the transmission of HIV and drug resistance

BACKGROUND

Attrition due to loss to follow-up or termination of antiretroviral therapy (ART) among HIV-infected patients in care may increase the risk of emergence and transmission of drug resistance (TDR), diminish benefit of treatment, and increase morbidity and mortality. Understanding the impact of attrition on the epidemic is essential to provide interventions for improving retention in care.

METHODS

We developed a comprehensive HIV transmission dynamics model by considering CD4 + cell count dependent diagnosis, treatment, and attrition involving TDR and acquired drug resistance. The model was calibrated by 11 groups HIV/AIDS surveillance data during 2008-2018 from Guangxi, China, and validated by the prevalence of TDR among diagnosed treatment-naive individuals. We aimed to investigate how attrition would affect the transmission of HIV and drug-resistance when expanding ART.

RESULTS

In the base case with CD4 + cell count dependent per capita attrition rates 0.025∼0.15 and treatment rates 0.23∼0.42, we projected cumulative total new infections, new drug-resistant infections, and HIV-related deaths over 2022-2030 would be 145 391, 7637, and 51 965, respectively. Increasing treatment rates by 0.1∼0.2 can decrease the above total new infections (deaths) by 1.63∼2.93% (3.52∼6.16%). However, even 0.0114∼0.0220 (0.0352∼0.0695) increase in attrition rates would offset this benefit of decreasing infections (deaths). Increasing treatment rates (attrition rates) by 0.05∼0.1 would increase the above drug-resistant infections by 0.16∼0.30% (22.18∼41.15%).

CONCLUSION

A minor increase in attrition can offset the benefit of treatment expansion and increase the transmission of HIV drug resistance. Reducing attrition rates for patients already in treatment may be as important as expanding treatment for untreated patients.

A network immuno-epidemiological model of HIV and opioid epidemics

In this paper, we introduce a novel multi-scale network model of two epidemics: HIV infection and opioid addiction. The HIV infection dynamics is modeled on a complex network. We determine the basic reproduction number of HIV infection, $ \mathcal{R}_{v} $, and the basic reproduction number of opioid addiction, $ \mathcal{R}_{u} $. We show that the model has a unique disease-free equilibrium which is locally asymptotically stable when both $ \mathcal{R}_{u} $ and $ \mathcal{R}_{v} $ are less than one. If $ \mathcal{R}_{u} > 1 $ or $ \mathcal{R}_{v} > 1 $, then the disease-free equilibrium is unstable and there exists a unique semi-trivial equilibrium corresponding to each disease. The unique opioid only equilibrium exist when the basic reproduction number of opioid addiction is greater than one and it is locally asymptotically stable when the invasion number of HIV infection, $ \mathcal{R}^{1}_{v_i} $ is less than one. Similarly, the unique HIV only equilibrium exist when the basic reproduction number of HIV is greater than one and it is locally asymptotically stable when the invasion number of opioid addiction, $ \mathcal{R}^{2}_{u_i} $ is less than one. Existence and stability of co-existence equilibria remains an open problem. We performed numerical simulations to better understand the impact of three epidemiologically important parameters that are at the intersection of two epidemics: $ q_v $ the likelihood of an opioid user being infected with HIV, $ q_u $ the likelihood of an HIV-infected individual becoming addicted to opioids, and $ \delta $ recovery from opioid addiction. Simulations suggest that as the recovery from opioid use increases, the prevalence of co-affected individuals, those who are addicted to opioids and are infected with HIV, increase significantly. We demonstrate that the dependence of the co-affected population on $ q_u $ and $ q_v $ are not monotone.

Immuno-epidemiological co-affection model of HIV infection and opioid addiction

In this paper, we present a multi-scale co-affection model of HIV infection and opioid addiction. The population scale epidemiological model is linked to the within-host model which describes the HIV and opioid dynamics in a co-affected individual. CD4 cells and viral load data obtained from morphine addicted SIV-infected monkeys are used to validate the within-host model. AIDS diagnoses, HIV death and opioid mortality data are used to fit the between-host model. When the rates of viral clearance and morphine uptake are fixed, the within-host model is structurally identifiable. If in addition the morphine saturation and clearance rates are also fixed the model becomes practical identifiable. Analytical results of the multi-scale model suggest that in addition to the disease-addiction-free equilibrium, there is a unique HIV-only and opioid-only equilibrium. Each of the boundary equilibria is stable if the invasion number of the other epidemic is below one. Elasticity analysis suggests that the most sensitive number is the invasion number of opioid epidemic with respect to the parameter of enhancement of HIV infection of opioid-affected individual. We conclude that the most effective control strategy is to prevent opioid addicted individuals from getting HIV, and to treat the opioid addiction directly and independently from HIV.

The dynamics of sexually transmitted diseases with men who have sex with men

In this paper, we give a rather complete analysis for a susceptible-infective sexually transmitted disease (STD) model, where the males are divided into two different groups based on their different sexual orientation. The threshold [Formula: see text] of STD model is obtained. If [Formula: see text], the disease-free equilibrium is globally asymptotically stable. Further, we investigate the existence and stability of the boundary equilibria that characterize the males of the different sexual orientation. We also investigate the existence and stability of the positive equilibrium, which characterizes the possibility of coexistence of male heterosexual and male homosexual. We obtain sufficient and necessary conditions for the existence and global stability of these equilibria. We see that the proportion of heterosexuality in MSM affects the stability of the system. The theoretical results are verified by numerical simulation.

Modeling and Research on an Immuno-Epidemiological Coupled System with Coinfection

In this paper, a two-strain model with coinfection that links immunological and epidemiological dynamics across scales is formulated. On the with-in host scale, the two strains eliminate each other with the strain having the larger immunological reproduction number persisting. However, on the population scale coinfection is a common occurrence. Individuals infected with strain one can become coinfected with strain two and similarly for individuals originally infected with strain two. The immunological reproduction numbers \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{j}$$\end{document}Rj, the epidemiological reproduction numbers \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_{j}$$\end{document}Rj and invasion reproduction numbers \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_{j}^{i}$$\end{document}Rji are computed. Besides the disease-free equilibrium, there are strain one and strain two dominance equilibria. The disease-free equilibrium is locally asymptotically stable when the epidemiological reproduction numbers \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_{j}$$\end{document}Rj are smaller than one. In addition, each strain dominance equilibrium is locally asymptotically stable if the corresponding epidemiological reproduction number is larger than one and the invasion reproduction number of the other strain is smaller than one. The coexistence equilibrium exists when all the reproduction numbers are greater than one. Simulations suggest that when both invasion reproduction numbers are smaller than one, bistability occurs with one of the strains persisting or the other, depending on initial conditions.

Global analysis of an environmental disease transmission model linking within-host and between-host dynamics

In this paper, a multi-scale mathematical model for environmentally transmitted diseases is proposed which couples the pathogen-immune interaction inside the human body with the disease transmission at the population level. The model is based on the nested approach that incorporates the infection-age-structured immunological dynamics into an epidemiological system structured by the chronological time, the infection age and the vaccination age. We conduct detailed analysis for both the within-host and between-host disease dynamics. Particularly, we derive the basic reproduction number R ₀ for the between-host model and prove the uniform persistence of the system. Furthermore, using carefully constructed Lyapunov functions, we establish threshold-type results regarding the global dynamics of the between-host system: the disease-free equilibrium is globally asymptotically stable when R ₀ < 1, and the endemic equilibrium is globally asymptotically stable when R ₀ > 1. We explore the connection between the within-host and between-host dynamics through both mathematical analysis and numerical simulation. We show that the pathogen load and immune strength at the individual level contribute to the disease transmission and spread at the population level. We also find that, although the between-host transmission risk correlates positively with the within-host pathogen load, there is no simple monotonic relationship between the disease prevalence and the individual pathogen load.