Modeling the progression of Type 2 diabetes with underlying obesity.

Environmentally induced or epigenetic-related beta-cell dysfunction and insulin resistance play a critical role in the progression to diabetes. We developed a mathematical modeling framework capable of studying the progression to diabetes incorporating various diabetogenic factors. Considering the heightened risk of beta-cell defects induced by obesity, we focused on the obesity-diabetes model to further investigate the influence of obesity on beta-cell function and glucose regulation. The model characterizes individualized glucose and insulin dynamics over the span of a lifetime. We then fit the model to the longitudinal data of the Pima Indian population, which captures both the fluctuations and long-term trends of glucose levels. As predicted, controlling or eradicating the obesity-related factor can alleviate, postpone, or even reverse diabetes. Furthermore, our results reveal that distinct abnormalities of beta-cell function and levels of insulin resistance among individuals contribute to different risks of diabetes. This study may encourage precise interventions to prevent diabetes and facilitate individualized patient treatment.

HIV infection dynamics and viral rebound: Modeling results from humanized mice.

Despite years of combined antiretroviral therapy (cART), HIV persists in infected individuals. The virus also rebounds after the cessation of cART. The sources contributing to viral persistence and rebound are not fully understood. When viral rebound occurs, what affects the time to rebound and how to delay the rebound remain unclear. In this paper, we started with the data fitting of an HIV infection model to the viral load data in treated and untreated humanized myeloid-only mice (MoM) in which macrophages serve as the target of HIV infection. By fixing the parameter values for macrophages from the MoM fitting, we fit a mathematical model including the infection of two target cell populations to the viral load data from humanized bone marrow/liver/thymus (BLT) mice, in which both CD4+ T cells and macrophages are the target of HIV infection. Data fitting suggests that the viral load decay in BLT mice under treatment has three phases. The loss of infected CD4+ T cells and macrophages is a major contributor to the first two phases of viral decay, and the last phase may be due to the latent infection of CD4+ T cells. Numerical simulations using parameter estimates from the data fitting show that the pre-ART viral load and the latent reservoir size at treatment cessation can affect viral growth rate and predict the time to viral rebound. Model simulations further reveal that early and prolonged cART can delay the viral rebound after cessation of treatment, which may have implications in the search for functional control of HIV infection.

A multi-strain model with asymptomatic transmission: Application to COVID-19 in the US.

COVID-19, induced by the SARS-CoV-2 infection, has caused an unprecedented pandemic in the world. New variants of the virus have emerged and dominated the virus population. In this paper, we develop a multi-strain model with asymptomatic transmission to study how the asymptomatic or pre-symptomatic infection influences the transmission between different strains and control strategies that aim to mitigate the pandemic. Both analytical and numerical results reveal that the competitive exclusion principle still holds for the model with the asymptomatic transmission. By fitting the model to the COVID-19 case and viral variant data in the US, we show that the omicron variants are more transmissible but less fatal than the previously circulating variants. The basic reproduction number for the omicron variants is estimated to be 11.15, larger than that for the previous variants. Using mask mandate as an example of non-pharmaceutical interventions, we show that implementing it before the prevalence peak can significantly lower and postpone the peak. The time of lifting the mask mandate can affect the emergence and frequency of subsequent waves. Lifting before the peak will result in an earlier and much higher subsequent wave. Caution should also be taken to lift the restriction when a large portion of the population remains susceptible. The methods and results obtained her e may be applied to the study of the dynamics of other infectious diseases with asymptomatic transmission using other control measures.

A two-sex model of human papillomavirus infection: Vaccination strategies and a case study.

Vaccination is effective in preventing human papillomavirus (HPV) infection. It still remains debatable whether males should be included in a vaccination program and unclear how to allocate the vaccine in genders to achieve the maximum benefits. In this paper, we use a two-sex model to assess HPV vaccination strategies and use the data from Guangxi Province in China as a case study. Both mathematical analysis and numerical simulations show that the basic reproduction number, an important indicator of the transmission potential of the infection, achieves its minimum when the priority of vaccination is given to the gender with a smaller recruit rate. Given a fixed amount of vaccine, splitting the vaccine evenly usually leads to a larger basic reproduction number and a higher prevalence of infection. Vaccination becomes less effective in reducing the infection once the vaccine amount exceeds the smaller recruit rate of the two genders. In the case study, we estimate the basic reproduction number is 1.0333 for HPV 16/18 in people aged 15-55. The minimal bivalent HPV vaccine needed for the disease prevalence to be below 0.05% is 24050 per year, which should be given to females. However, with this vaccination strategy it would require a very long time and a large amount of vaccine to achieve the goal. In contrast with allocating the same vaccine amount every year, we find that a variable vaccination strategy with more vaccine given in the beginning followed by less vaccine in later years can save time and total vaccine amount. The variable vaccination strategy illustrated in this study can help to better distribute the vaccine to reduce the HPV prevalence. Although this work is for HPV infection and the case study is for a province in China, the model, analysis and conclusions may be applicable to other sexually transmitted diseases in other regions or countries.

The impact of supplementary immunization activities on measles transmission dynamics and implications for measles elimination goals: A mathematical modelling study.

BACKGROUND: Measles has re-emerged globally due to the accumulation of susceptible individuals and immunity gap, which causes challenges in eliminating measles. Routine vaccination and supplementary immunization activities (SIAs) have greatly improved measles control, but the impact of SIAs on the measles transmission dynamics remains unclear as the vaccine-induced immunity wanes. METHODS: We developed a comprehensive measles transmission dynamics model by taking into account population demographics, age-specific contact patterns, seasonality, routine vaccination, SIAs, and the waning vaccine-induced immunity. The model was calibrated by the monthly age-specific cases data from 2005 to 2018 in Jiangsu Province, China, and validated by the dynamic sero-prevalence data. We aimed to investigate the short-term and long-term impact of three-time SIAs during 2009-2012 (9.68 million and 4.25 million children aged 8 months-14 years in March 2009 and September 2010, respectively, and 140,000 children aged 8 months-6 years in March 2012) on the measles disease burden and explored whether additional SIAs could accelerate the measles elimination. RESULTS: We estimated that the cumulative numbers of measles cases from March 2009 to December 2012 (in the short run) and to December 2018 (in the long run) after three-time SIAs (base case) were 6,699 (95% confidence interval [CI]: 2,928-10,469), and 22,411 (15,146-29,675), which averted 45.0% (42.9%-47.0%) and 34.3% (30.7%-37.9%) of 12,226 (4,916-19,537) and 34,274 (21,350-47,199) cases without SIAs, respectively. The fraction of susceptibles for children aged 8-23 months and 2-14 years decreased from 8.3% and 10.8% in March 2009 to 5.8% and 5.8% in April 2012, respectively. However, the fraction of susceptibles aged 15-49 years and above 50 years increased gradually to about 15% in 2018 irrespective of SIAs due to the waning immunity. The measles elimination goal would be reached in 2028, and administrating additional one-off SIAs in September 2022 to children aged 8-23 months, or young adolescents aged 15-19 years could accelerate the elimination one year earlier. CONCLUSIONS: SIAs have greatly reduced the measles incidence and the fraction of susceptibles, but the benefit may wane over time. Under the current interventions, Jiangsu province would reach the measles elimination goal in 2028. Additional SIAs may accelerate the measles elimination one year earlier.

A Multiscale Model of COVID-19 Dynamics.

COVID-19, caused by the infection of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has been a global pandemic and created unprecedented public health challenges throughout the world. Despite significant progresses in understanding the disease pathogenesis and progression, the epidemiological triad of pathogen, host, and environment remains unclear. In this paper, we develop a multiscale model to study the coupled within-host and between-host dynamics of COVID-19. The model includes multiple transmission routes (both human-to-human and environment-to-human) and connects multiple scales (both the population and individual levels). A detailed analysis on the local and global dynamics of the fast system, slow system and full system shows that rich dynamics, including both forward and backward bifurcations, emerge with the coupling of viral infection and epidemiological models. Model fitting to both virological and epidemiological data facilitates the evaluation of the influence of a few infection characteristics and antiviral treatment on the spread of the disease. Our work underlines the potential role that the environment can play in the transmission of COVID-19. Antiviral treatment of infected individuals can delay but cannot prevent the emergence of disease outbreaks. These results highlight the implementation of comprehensive intervention measures such as social distancing and wearing masks that aim to stop airborne transmission, combined with surface disinfection and hand hygiene that can prevent environmental transmission. The model also provides a multiscale modeling framework to study other infectious diseases when the environment can serve as a reservoir of pathogens.

The impact of vaccination on human papillomavirus infection with disassortative geographical mixing: a two-patch modeling study.

Human papillomavirus (HPV) infection can spread between regions. What is the impact of disassortative geographical mixing on the dynamics of HPV transmission? Vaccination is effective in preventing HPV infection. How to allocate HPV vaccines between genders within each region and between regions to reduce the total infection? Here we develop a two-patch two-sex model to address these questions. The control reproduction number [Formula: see text] under vaccination is obtained and shown to provide a critical threshold for disease elimination. Both analytical and numerical results reveal that disassortative geographical mixing does not affect [Formula: see text] and only has a minor impact on the disease prevalence in the total population given the vaccine uptake proportional to the population size for each gender in the two patches. When the vaccine uptake is not proportional to the population size, sexual mixing between the two patches can reduce [Formula: see text] and mitigate the consequence of disproportionate vaccine coverage. Using parameters calibrated from the data of a case study, we find that if the two patches have the same or similar sex ratios, allocating vaccines proportionally according to the new recruits in two patches and giving priority to the gender with a smaller recruit rate within each patch will bring the maximum benefit in reducing the total prevalence. We also show that a time-variable vaccination strategy between the two patches can further reduce the disease prevalence. This study provides some quantitative information that may help to develop vaccine distribution strategies in multiple regions with disassortative mixing.

Modeling HIV multiple infection.

Multiple infection of target cells by human immunodeficiency virus (HIV) may lead to viral escape from host immune responses and drug resistance to antiretroviral therapy, bringing more challenges to the control of infection. The mechanisms underlying HIV multiple infection and their relative contributions are not fully understood. In this paper, we develop and analyze a mathematical model that includes sequential cell-free virus infection (i.e.one virus is transmitted each time in a sequential infection of target cells by virus) and cell-to-cell transmission (i.e.multiple viral genomes are transmitted simultaneously from infected to uninfected cells). By comparing model prediction with the distribution data of proviral genomes in HIV-infected spleen cells, we find that multiple infection can be well explained when the two modes of viral transmission are both included. Numerical simulation using the parameter estimates from data fitting shows that the majority of T cell infections are attributed to cell-to-cell transmission and this transmission mode also accounts for more than half of cell's multiple infections. These results suggest that cell-to-cell transmission plays a critical role in forming HIV multiple infection and thus has important implications for HIV evolution and pathogenesis.

A unified mathematical model of thyroid hormone regulation and implication for personalized treatment of thyroid disorders.

Current clinician practice for thyroid hormone regulation of patients is based upon guesswork and experience rather than quantified analysis, which exposes patients under longer risk and discomfort. To quantitatively analyze the thyroid regulation for patients of different thyroid states, we develop a two-dimensional mathematical model that can be applied to analyze the dynamic behaviors of thyroid hormones with or without drug intervention. The unified model can be employed to study the regulation of TSH (thyroid-stimulating hormone) and FT4 (free thyroxine) for euthyroid (normal thyroid) subjects, Hashimoto's thyroiditis, and Graves' disease patients, respectively. The results suggest that the level of TPOAb (thyroid peroxidase antibody) may be a factor determining whether the patient would progress from euthyroid state to subclinical or clinical hypothyroidism, and that increased TRAb (TSH receptor antibody) may lead Graves' disease to deteriorate from the early stage to overt hyperthyroidism. Given the early blood-test data, we demonstrate the feasibility for healthcare professionals to apply our model in choosing an appropriate dosage regimen for patients to achieve the desired TSH and FT4 levels within a specified time frame. This proposed model has the potential to optimize personalized treatment and shorten the therapeutic time for patients suffering from Hashimoto's thyroiditis and Graves' disease.

Effects of New York's Executive Order on Face Mask Use on COVID-19 Infections and Mortality: A Modeling Study.

There is growing evidence on the effect of face mask use in controlling the spread of COVID-19. However, few studies have examined the effect of local face mask policies on the pandemic. In this study, we developed a dynamic compartmental model of COVID-19 transmission in New York City (NYC), which was the epicenter of the COVID-19 pandemic in the USA. We used data on daily and cumulative COVID-19 infections and deaths from the NYC Department of Health and Mental Hygiene to calibrate and validate our model. We then used the model to assess the effect of the executive order on face mask use on infections and deaths due to COVID-19 in NYC. Our results showed that the executive order on face mask use was estimated to avert 99,517 (95% CIs 72,723-126,312) COVID-19 infections and 7978 (5692-10,265) deaths in NYC. If the executive order was implemented 1 week earlier (on April 10), the averted infections and deaths would be 111,475 (81,593-141,356) and 9017 (6446-11,589), respectively. If the executive order was implemented 2 weeks earlier (on April 3 when the Centers for Disease Control and Prevention recommended face mask use), the averted infections and deaths would be 128,598 (94,373-162,824) and 10,515 (7540-13,489), respectively. Our study provides public health practitioners and policymakers with evidence on the importance of implementing face mask policies in local areas as early as possible to control the spread of COVID-19 and reduce mortality.

A Dynamic Model to Assess Human Papillomavirus Vaccination Strategies in a Heterosexual Population Combined with Men Who have Sex with Men.

Vaccination is effective in preventing human papillomavirus (HPV) infection. It is imperative to investigate who should be vaccinated and what the best vaccine distribution strategy is. In this paper, we use a dynamic model to assess HPV vaccination strategies in a heterosexual population combined with gay, bisexual, and other men who have sex with men (MSM). The basic reproduction numbers for heterosexual females, heterosexual males and MSM as well as their average for the total population are obtained. We also derive a threshold parameter, based on basic reproduction numbers, for model analysis. From the analysis and numerical investigations, we have several conclusions. (1) To eliminate HPV infection, the priority of vaccination should be given to MSM, especially in countries that have already achieved high coverage in females. The heterosexual population gets great benefit but MSM only get minor benefit from vaccinating heterosexual females or males. (2) The best vaccination strategy is to vaccinate MSM firstly as many as possible, then heterosexual females, lastly heterosexual males. (3) Given a fixed vaccination coverage of MSM, distributing the remaining vaccines to only heterosexual females or males leads to a similar prevalence in the total population. This prevalence is lower than that when vaccines are distributed to both genders. The evener the distribution, the higher the prevalence in the total population. (4) Vaccination becomes less effective in reducing the prevalence as more vaccines are given. It is more effective to allocate vaccines to a region with lower vaccination coverage. This study provides information that may help policymakers formulate guidelines for vaccine distribution to reduce HPV prevalence on the basis of vaccine availability and prior vaccination coverage. Whether these guidelines are affected when the objective is to reduce HPV-associated cancer incidence remains to be further studied.

Dynamics of a new HIV model with the activation status of infected cells.

The activation status can dictate the fate of an HIV-infected CD4+ T cell. Infected cells with a low level of activation remain latent and do not produce virus, while cells with a higher level of activation are more productive and thus likely to transfer more virions to uninfected cells during cell-to-cell transmission. How the activation status of infected cells affects HIV dynamics under antiretroviral therapy remains unclear. We develop a new mathematical model that structures the population of infected cells continuously according to their activation status. The effectiveness of antiretroviral drugs in blocking cell-to-cell viral transmission decreases as the level of activation of infected cells increases because the more virions are transferred from infected to uninfected cells during cell-to-cell transmission, the less effectively the treatment is able to inhibit the transmission. The basic reproduction number [Formula: see text] of the model is shown to determine the existence and stability of the equilibria. Using the principal spectral theory and comparison principle, we show that the infection-free equilibrium is locally and globally asymptotically stable when [Formula: see text] is less than one. By constructing Lyapunov functional, we prove that the infected equilibrium is globally asymptotically stable when [Formula: see text] is greater than one. Numerical investigation shows that even when treatment can completely block cell-free virus infection, virus can still persist due to cell-to-cell transmission. The random switch between infected cells with different activation levels can also contribute to the replenishment of the latent reservoir, which is considered as a major barrier to viral eradication. This study provides a new modeling framework to study the observations, such as the low viral load persistence, extremely slow decay of latently infected cells and transient viral load measurements above the detection limit, in HIV-infected patients during suppressive antiretroviral therapy.

Investigating the relationship between reopening the economy and implementing control measures during the COVID-19 pandemic.

OBJECTIVES: The COVID-19 pandemic has resulted in an enormous burden on population health and the economy around the world. Although most cities in the United States have reopened their economies from previous lockdowns, it was not clear how the magnitude of different control measures-such as face mask use and social distancing-may affect the timing of reopening the economy for a local region. This study aimed to investigate the relationship between reopening dates and control measures and identify the conditions under which a city can be reopened safely. STUDY DESIGN: This was a mathematical modeling study. METHODS: We developed a dynamic compartment model to capture the transmission dynamics of COVID-19 in New York City. We estimated model parameters from local COVID-19 data. We conducted three sets of policy simulations to investigate how different reopening dates and magnitudes of control measures would affect the COVID-19 epidemic. RESULTS: The model estimated that maintaining social contact at 80% of the prepandemic level and a 50% face mask usage would prevent a major surge of COVID-19 after reopening. If social distancing were completely relaxed after reopening, face mask usage would need to be maintained at nearly 80% to prevent a major surge. CONCLUSIONS: Adherence to social distancing and increased face mask usage are keys to prevent a major surge after a city reopens its economy. The findings from our study can help policymakers identify the conditions under which a city can be reopened safely.

Modeling the role of macrophages in HIV persistence during antiretroviral therapy.

HIV preferentially infects activated CD4+ T cells. Current antiretroviral therapy cannot eradicate the virus. Viral infection of other cells such as macrophages may contribute to viral persistence during antiretroviral therapy. In addition to cell-free virus infection, macrophages can also get infected when engulfing infected CD4+ T cells as innate immune sentinels. How macrophages affect the dynamics of HIV infection remains unclear. In this paper, we develop an HIV model that includes the infection of CD4+ T cells and macrophages via cell-free virus infection and cell-to-cell viral transmission. We derive the basic reproduction number and obtain the local and global stability of the steady states. Sensitivity and viral dynamics simulations show that even when the infection of CD4+ T cells is completely blocked by therapy, virus can still persist and the steady-state viral load is not sensitive to the change of treatment efficacy. Analysis of the relative contributions to viral replication shows that cell-free virus infection leads to the majority of macrophage infection. Viral transmission from infected CD4+ T cells to macrophages during engulfment accounts for a small fraction of the macrophage infection and has a negligible effect on the total viral production. These results suggest that macrophage infection can be a source contributing to HIV persistence during suppressive therapy. Improving drug efficacies in heterogeneous target cells is crucial for achieving HIV eradication in infected individuals.

Within-Host Viral Dynamics in a Multi-compartmental Environment.

The discrepancy in the turnover of cells and virus in different organs or viral reservoirs necessitates the investigation of multiple compartments within a host. Establishing a multi-compartmental structure that describes the complexity of various organs, where viral infection comprehensively proceeds, provides a modeling framework for exploring the effect of spatial heterogeneity on viral dynamics. To successfully suppress within-host viral replication, it is imperative to determine drug administration during therapy, particularly for a combination of antiretroviral drugs. The proposed model provides quantitative insights into pharmacokinetics and the resulting virus population, which substantially relates to environmental heterogeneity. The main results are the following: (1) A model incorporating drug treatment admits threshold dynamics, driving to either viral extinction or uniform persistence, regardless of non-trivial initial infection, in the entire system. (2) Viral infection may be underestimated if a well-mixed (single-compartmental) model is used. (3) Optimal drug administration depends not only on the drug distribution over various compartments but also on the timing, described by phase shifts, of the administration of different drugs in a combined therapy.

The cost-effectiveness of oral HIV pre-exposure prophylaxis and early antiretroviral therapy in the presence of drug resistance among men who have sex with men in San Francisco.

BACKGROUND: Poor adherence to either antiretroviral treatment (ART) or pre-exposure prophylaxis (PrEP) can promote drug resistance, though this risk is thought to be considerably higher for ART. In the population of men who have sex with men (MSM) in San Francisco, PrEP coverage reached 9.6% in 2014 and has continued to rise. Given the risk of drug resistance and high cost of second-line drugs, the costs and benefits of initiating ART earlier while expanding PrEP coverage remain unclear. METHODS: We develop an infection-age-structured mathematical model and fit this model to the annual incidence of AIDS cases and deaths directly, and to resistance and demographic data indirectly. We investigate the impact of six various intervention scenarios (low, medium, or high PrEP coverage, with or without earlier ART) over the next 20 years. RESULTS: Low (medium, high) PrEP coverage with earlier ART could prevent 22% (42%, 57%) of a projected 44,508 total new infections and 8% (26%, 41%) of a projected 18,426 new drug-resistant infections, and result in a gain of 43,649 (74,048, 103,270) QALYs over 20 years compared to the status quo, at a cost of $4745 ($78,811, $115,320) per QALY gained, respectively. CONCLUSIONS: High PrEP coverage with earlier ART is expected to provide the greatest benefit but also entail the highest costs among the strategies considered. This strategy is cost-effective for the San Francisco MSM population, even considering the acquisition and transmission of ART-mediated drug resistance. However, without a substantial increase to San Francisco's annual HIV budget, the most advisable strategy may be initiating ART earlier, while maintaining current strategies of PrEP enrollment.

Early antiretroviral therapy and potent second-line drugs could decrease HIV incidence of drug resistance.

Early initiation of antiretroviral therapy (ART) reduces the risk of drug-sensitive HIV transmission but may increase the transmission of drug-resistant HIV. We used a mathematical model to estimate the long-term population-level benefits of ART and determine the scenarios under which earlier ART (treatment at 1 year post-infection, on average) could decrease simultaneously both total and drug-resistant HIV incidence (new infections). We constructed an infection-age-structured mathematical model that tracked the transmission rates over the course of infection and modelled the patients' life expectancy as a function of ART initiation timing. We fitted this model to the annual AIDS incidence and death data directly, and to resistance data and demographic data indirectly among men who have sex with men (MSM) in San Francisco. Using counterfactual scenarios, we assessed the impact on total and drug-resistant HIV incidence of ART initiation timing, frequency of acquired drug resistance, and second-line drug effectiveness (defined as the combination of resistance monitoring, biomedical drug efficacy and adherence). Earlier ART initiation could decrease the number of both total and drug-resistant HIV incidence when second-line drug effectiveness is sufficiently high (greater than 80%), but increase the proportion of new infections that are drug resistant. Thus, resistance may paradoxically appear to be increasing while actually decreasing.

Influence of raltegravir intensification on viral load and 2-LTR dynamics in HIV patients on suppressive antiretroviral therapy.

Antiretroviral therapy can suppress HIV-1 plasma viral load to below the detection limit but cannot eradicate the virus. Whether residual ongoing viral replication persists during suppressive therapy remains unclear. A few clinical studies showed that treatment intensification with an additional drug led to a lower viral load or an increase in 2-LTR (long terminal repeat), a marker for ongoing viral replication. However, some other studies found no change in the viral load and 2-LTR. In this paper, we developed multi-stage models to evaluate the influence of treatment intensification with the integrase inhibitor raltegravir on viral load and 2-LTR dynamics in HIV patients under suppressive therapy. We analyzed one model and obtained the local and global stability of the steady states. The model and its variation predict that raltegravir intensification induces a very minor decrease in the viral load and a minor increase in 2-LTR. We also compared modeling prediction with the 2-LTR data in a raltegravir intensification study. To achieve the 2-LTR increase observed in some patients, the level of viral replication needs to be substantially high, which is inconsistent with the sustained viral suppression in patients during treatment intensification. These modeling results, together with the theoretical estimate of the upper bound of the 2-LTR increase, suggest that treatment intensification with raltegravir has a minor effect on the plasma viremia and 2-LTR in patients under suppressive therapy. Other treatment strategies have to be developed for the cure or functional control of the infection.

Modeling the Slow CD4+ T Cell Decline in HIV-Infected Individuals.

The progressive loss of CD4+ T cell population is the hallmark of HIV-1 infection but the mechanism underlying the slow T cell decline remains unclear. Some recent studies suggested that pyroptosis, a form of programmed cell death triggered during abortive HIV infection, is associated with the release of inflammatory cytokines, which can attract more CD4+ T cells to be infected. In this paper, we developed mathematical models to study whether this mechanism can explain the time scale of CD4+ T cell decline during HIV infection. Simulations of the models showed that cytokine induced T cell movement can explain the very slow decline of CD4+ T cells within untreated patients. The long-term CD4+ T cell dynamics predicted by the models were shown to be consistent with available data from patients in Rio de Janeiro, Brazil. Highly active antiretroviral therapy has the potential to restore the CD4+ T cell population but CD4+ response depends on the effectiveness of the therapy, when the therapy is initiated, and whether there are drug sanctuary sites. The model also showed that chronic inflammation induced by pyroptosis may facilitate persistence of the HIV latent reservoir by promoting homeostatic proliferation of memory CD4+ cells. These results improve our understanding of the long-term T cell dynamics in HIV-1 infection, and support that new treatment strategies, such as the use of caspase-1 inhibitors that inhibit pyroptosis, may maintain the CD4+ T cell population and reduce the latent reservoir size.

Dynamics of an HIV Model with Multiple Infection Stages and Treatment with Different Drug Classes.

Highly active antiretroviral therapy can effectively control HIV replication in infected individuals. Some clinical and modeling studies suggested that viral decay dynamics may depend on the inhibited stages of the viral replication cycle. In this paper, we develop a general mathematical model incorporating multiple infection stages and various drug classes that can interfere with specific stages of the viral life cycle. We derive the basic reproductive number and obtain the global stability results of steady states. Using several simple cases of the general model, we study the effect of various drug classes on the dynamics of HIV decay. When drugs are assumed to be 100% effective, drugs acting later in the viral life cycle lead to a faster or more rapid decay in viremia. This is consistent with some patient and experimental data, and also agrees with previous modeling results. When drugs are not 100% effective, the viral decay dynamics are more complicated. Without a second population of long-lived infected cells, the viral load decline can have two phases if drugs act at an intermediate stage of the viral replication cycle. The slopes of viral load decline depend on the drug effectiveness, the death rate of infected cells at different stages, and the transition rate of infected cells from one to the next stage. With a second population of long-lived infected cells, the viral load decline can have three distinct phases, consistent with the observation in patients receiving antiretroviral therapy containing the integrase inhibitor raltegravir. We also fit modeling prediction to patient data under efavirenz (a nonnucleoside reverse-transcriptase inhibitor) and raltegravir treatment. The first-phase viral load decline under raltegravir therapy is longer than that under efavirenz, resulting in a lower viral load at initiation of the second-phase decline in patients taking raltegravir. This explains why patients taking a raltegravir-based therapy were faster to achieve viral suppression than those taking an efavirenz-based therapy. Taken together, this work provides a quantitative and systematic comparison of the effect of different drug classes on HIV decay dynamics and can explain the viral load decline in HIV patients treated with raltegravir-containing regimens.