Modeling the effects of drugs of abuse on within-host dynamics of two HIV species.

Injection drug use is one of the most significant risk factors associated with contracting human immunodeficiency virus (HIV), and drug users infected with HIV suffer from a higher viral load and rapid disease progression. While replication of HIV may result in many mutant viruses that can escape recognition of the host's immune response, the presence of morphine (a drug of abuse) can decrease the viral mutation rate and cellular immune responses. This study develops a mathematical model to explore the effects of morphine-altered mutation and cellular immune response on the within-host dynamics of two HIV species, a wild-type and a mutant. Our model predicts that the morphine-altered mutation rate and cellular immune response allow the wild-type virus to outcompete the mutant virus, resulting in a higher set point viral load and lower CD4 count. We also compute the basic reproduction numbers and show that the dominant species is determined by morphine concentration, with the mutant dominating below and the wild-type dominating above a threshold. Furthermore, we identified three biologically relevant equilibria, infection-free, mutant-only, and coexistence, which are completely characterized by the fitness cost of mutation, mutant escape rate, and morphine concentration.

Data-driven models for the risk of infection and hospitalization during a pandemic: Case study on COVID-19 in Nepal.

The newly emerging pandemic disease often poses unexpected troubles and hazards to the global health system, particularly in low and middle-income countries like Nepal. In this study, we developed mathematical models to estimate the risk of infection and the risk of hospitalization during a pandemic which are critical for allocating resources and planning health policies. We used our models in Nepal's unique data set to explore national and provincial-level risks of infection and risk of hospitalization during the Delta and Omicron surges. Furthermore, we used our model to identify the effectiveness of non-pharmaceutical interventions (NPIs) to mitigate COVID-19 in various groups of people in Nepal. Our analysis shows no significant difference in reproduction numbers in provinces between the Delta and Omicron surge periods, but noticeable inter-provincial disparities in the risk of infection (for example, during Delta (Omicron) surges, the risk of infection of Bagmati province is: ∼ 98.94 (89.62); Madhesh province: ∼ 12.16 (5.1); Karnali province ∼31.16 (3) per hundred thousands). Our estimates show a significantly low level of hospitalization risk during the Omicron surge compared to the Delta surge (hospitalization risk is: ∼10% in Delta and ∼2.5% in Omicron). We also found significant inter-provincial disparities in the hospitalization rate (for example, ∼ 6% in Madhesh province and ∼ 21% in Sudur Paschim) during the Delta surge. Moreover, our results show that closing only schools, colleges, and workplaces reduces the risk of infection by one-third, while a complete lockdown reduces the infections by two-thirds. Our study provides a framework for the computation of the risk of infection and the risk of hospitalization and offers helpful information for controlling the pandemic.

Modeling Antiretrovial Treatment to Mitigate HIV in the Brain: Impact of the Blood-Brain Barrier.

Current research in Human Immunodeficiency Virus (HIV) focuses on eradicating virus reservoirs that prevent or dampen the effectiveness of antiretroviral treatment (ART). One such reservoir, the brain, reduces treatment efficacy via the blood-brain barrier (BBB), causing an obstacle to drug penetration into the brain. In this study, we develop a mathematical model to examine the impact of the BBB on ART effectiveness for mitigating brain HIV. A thorough analysis of the model allowed us to fully characterize the global threshold dynamics with the viral clearance and persistence in the brain for the basic reproduction number less than unity and greater than unity, respectively. Our model showed that the BBB has a significant role in inhibiting the effect of ART within the brain despite the effective viral load suppression in the plasma. The level of impact, however, depends on factors such as the CNS Penetration Effectiveness (CPE) score, the slope of the drug dose-response curves, the ART initiation timing, and the number of drugs in the ART protocol. These results suggest that reducing the plasma viral load to undetectable levels due to some drug regimen may not necessarily indicate undetectable levels of HIV in the brain. Thus, the effect of the BBB on viral suppression in the brain must be considered for developing proper treatment protocols against HIV infection.

Time scale theory on stability of explicit and implicit discrete epidemic models: applications to Swine flu outbreak.

Time scales theory has been in use since the 1980s with many applications. Only very recently, it has been used to describe within-host and between-hosts dynamics of infectious diseases. In this study, we present explicit and implicit discrete epidemic models motivated by the time scales modeling approach. We use these models to formulate the basic reproduction number, which determines whether an outbreak occurs or the disease dies out. We discuss the stability of the disease-free and endemic equilibrium points using the linearization method and Lyapunov function. Furthermore, we apply our models to swine flu outbreak data to demonstrate that the discrete models can accurately describe the epidemic dynamics. Our comparison analysis shows that the implicit discrete model can best describe the data regardless of the data frequency. In addition, we perform the sensitivity analysis on the key parameters of the models to study how these parameters impact the basic reproduction number.

Early events in hepatitis B infection: the role of inoculum dose.

The relationship between the inoculum dose and the ability of the pathogen to invade the host is poorly understood. Experimental studies in non-human primates infected with different inoculum doses of hepatitis B virus have shown a non-monotonic relationship between dose magnitude and infection outcome, with high and low doses leading to 100% liver infection and intermediate doses leading to less than 0.1% liver infection, corresponding to CD4 T-cell priming. Since hepatitis B clearance is CD8 T-cell mediated, the question of whether the inoculum dose influences CD8 T-cell dynamics arises. To help answer this question, we developed a mathematical model of virus-host interaction following hepatitis B virus infection. Our model explains the experimental data well, and predicts that the inoculum dose affects both the timing of the CD8 T-cell expansion and the quality of its response, especially the non-cytotoxic function. We find that a low-dose challenge leads to slow CD8 T-cell expansion, weak non-cytotoxic functions, and virus persistence; high- and medium-dose challenges lead to fast CD8 T-cell expansion, strong cytotoxic and non-cytotoxic function, and virus clearance; while a super-low-dose challenge leads to delayed CD8 T-cell expansion, strong cytotoxic and non-cytotoxic function, and virus clearance. These results are useful for designing immune cell-based interventions.

Transmission dynamics of COVID-19 in Nepal: Mathematical model uncovering effective controls.

While most of the countries around the globe are combating the pandemic of COVID-19, the level of its impact is quite variable among different countries. In particular, the data from Nepal, a developing country having an open border provision with highly COVID-19 affected country India, has shown a biphasic pattern of epidemic, a controlled phase (until July 21, 2020) followed by an outgrown phase (after July 21, 2020). To uncover the effective strategies implemented during the controlled phase, we develop a mathematical model that is able to describe the data from both phases of COVID-19 dynamics in Nepal. Using our best parameter estimates with 95% confidence interval, we found that during the controlled phase most of the recorded cases were imported from outside the country with a small number generated from the local transmission, consistent with the data. Our model predicts that these successful strategies were able to maintain the reproduction number at around 0.21 during the controlled phase, preventing 442,640 cases of COVID-19 and saving more than 1,200 lives in Nepal. However, during the outgrown phase, when the strategies such as border screening and quarantine, lockdown, and detection and isolation, were altered, the reproduction number raised to 1.8, resulting in exponentially growing cases of COVID-19. We further used our model to predict the long-term dynamics of COVID-19 in Nepal and found that without any interventions the current trend may result in about 18.76 million cases (10.70 million detected and 8.06 million undetected) and 89 thousand deaths in Nepal by the end of 2021. Finally, using our predictive model, we evaluated the effects of various control strategies on the long-term outcome of this epidemics and identified ideal strategies to curb the epidemic in Nepal.

Modeling HIV-1 infection in the brain.

While highly active antiretroviral therapy (HAART) is successful in controlling the replication of Human Immunodeficiency Virus (HIV-1) in many patients, currently there is no cure for HIV-1, presumably due to the presence of reservoirs of the virus. One of the least studied viral reservoirs is the brain, which the virus enters by crossing the blood-brain barrier (BBB) via macrophages, which are considered as conduits between the blood and the brain. The presence of HIV-1 in the brain often leads to HIV associated neurocognitive disorders (HAND), such as encephalitis and early-onset dementia. In this study we develop a novel mathematical model that describes HIV-1 infection in the brain and in the plasma coupled via the BBB. The model predictions are consistent with data from macaques infected with a mixture of simian immunodeficiency virus (SIV) and simian-human immunodeficiency virus (SHIV). Using our model, we estimate the rate of virus transport across the BBB as well as viral replication inside the brain, and we compute the basic reproduction number. We also carry out thorough sensitivity analysis to define the robustness of the model predictions on virus dynamics inside the brain. Our model provides useful insight into virus replication within the brain and suggests that the brain can be an important reservoir causing long-term viral persistence.

Modeling Intracellular Delay in Within-Host HIV Dynamics Under Conditioning of Drugs of Abuse.

Drugs of abuse, such as opiates, have been widely associated with the enhancement of HIV replication, the acceleration of disease progression, and severe neuropathogenesis. Specifically, the presence of drugs of abuse (morphine) switches target cells (CD4[Formula: see text] T cells) from lower-to-higher susceptibility to HIV infection. The effect of such switching behaviors on viral dynamics may be altered due to the intracellular delay (the replication time between viral entry into a target cell and the production of new viruses by the infected cell). In this study, we develop, for the first time, a viral dynamics model that includes an intracellular delay under the conditioning of drugs of abuse. We parameterize the model using experimental data from simian immunodeficiency virus infection of morphine-addicted macaques. Results from thorough mathematical analyses and numerical simulations of our model show that the intracellular delay can play a significant role in HIV dynamics under the conditioning of drugs of abuse, particularly during the acute phase of infection. Our model and the related results provide new insights into the HIV dynamics and may help develop strategies to control HIV infections in drug abusers.

Modeling the Effects of Morphine on Simian Immunodeficiency Virus Dynamics.

Complications of HIV-1 infection in individuals who utilize drugs of abuse is a significant problem, because these drugs have been associated with higher virus replication and accelerated disease progression as well as severe neuropathogenesis. To gain further insight it is important to quantify the effects of drugs of abuse on HIV-1 infection dynamics. Here, we develop a mathematical model that incorporates experimentally observed effects of morphine on inducing HIV-1 co-receptor expression. For comparison we also considered viral dynamic models with cytolytic or noncytolytic effector cell responses. Based on the small sample size Akaike information criterion, these models were inferior to the new model based on changes in co-receptor expression. The model with morphine affecting co-receptor expression agrees well with the experimental data from simian immunodeficiency virus infections in morphine-addicted macaques. Our results show that morphine promotes a target cell subpopulation switch from a lower level of susceptibility to a state that is about 2-orders of magnitude higher in susceptibility to SIV infection. As a result, the proportion of target cells with higher susceptibility remains extremely high in morphine conditioning. Such a morphine-induced population switch not only has adverse effects on the replication rate, but also results in a higher steady state viral load and larger CD4 count drops. Moreover, morphine conditioning may pose extra obstacles to controlling viral load during antiretroviral therapy, such as pre-exposure prophylaxis and post infection treatments. This study provides, for the first time, a viral dynamics model, viral dynamics parameters, and related analytical and simulation results for SIV dynamics under drugs of abuse.

Immediate antiviral therapy appears to restrict resting CD4+ cell HIV-1 infection without accelerating the decay of latent infection.

HIV type 1 (HIV-1) persists within resting CD4(+) T cells despite antiretroviral therapy (ART). To better understand the kinetics by which resting cell infection (RCI) is established, we developed a mathematical model that accurately predicts (r = 0.65, P = 2.5 × 10(-4)) the initial frequency of RCI measured about 1 year postinfection, based on the time of ART initiation and the dynamic changes in viremia and CD4(+) T cells. In the largest cohort of patients treated during acute seronegative HIV infection (AHI) in whom RCI has been stringently quantified, we found that early ART reduced the generation of latently infected cells. Although RCI declined after the first year of ART in most acutely infected patients, there was a striking absence of decline when initial RCI frequency was less than 0.5 per million. Notably, low-level viremia was observed more frequently as RCI increased. Together these observations suggest that (i) the degree of RCI is directly related to the availability of CD4(+) T cells susceptible to HIV, whether viremia is controlled by the immune response and/or ART; and (ii) that two pools of infected resting CD4(+) T cells exist, namely, less stable cells, observable in patients in whom viremia is not well controlled in early infection, and extremely stable cells that are established despite early ART. These findings reinforce and extend the concept that new approaches will be needed to eradicate HIV infection, and, in particular, highlight the need to target the extremely small but universal, long-lived latent reservoir.

Impact of Tenofovir gel as a PrEP on HIV infection: a mathematical model.

Pre-exposure prophylaxis (PrEP) has been considered as one of the promising interventions for HIV infection as experiments on various groups and sites have reported its significant effectiveness. This study evaluates the effectiveness of Tenofovir gel, one of the widely used PrEPs for women, through a mathematical model. Our model has excellent agreement with the experimental data on the use of Tenofovir gel as a PrEP in South African women. Using our model, we estimate both male-to-female and female-to-male transmission rates with and without Tenofovir gel protection. Through these estimates we demonstrate that the use of Tenofovir gel as a PrEP can significantly reduce the reproduction numbers, new infections, and HIV prevalence in South Africa. Our results further show that the effectiveness of Tenofovir gel largely depends on the level of adherence to the gel and the proportion of women under gel coverage. Even though Tenofovir gel alone may not be able to eradicate the disease as indicated by our estimates of the reproduction numbers, together with other interventions, such as condom use, it can serve as a strong weapon to fight against HIV epidemics.

Modeling measles transmission in adults and children: Implications to vaccination for eradication.

Despite the availability of successful vaccines, measles outbreaks have occurred frequently in recent years, presumably due to the lack of proper vaccination implementation. Moreover, measles cases in adult groups, albeit small in number, indicate that the previously neglected adult group may need to be brought into vaccine coverage to achieve WHO's goal of measles eradication from the globe. In this study, we develop a novel transmission dynamics model to describe measles cases in adults and children to evaluate the role of adult infection in persistent measles cases and vaccination programs for eradication. Analysis of our model, validated by measles cases from outbreaks in Nepal, provides the vaccination reproduction number (conditions for measles eradication or persistence) and the role of contact network size. Our results highlight that while children are primary targets for measles outbreaks, a small number of infections in adults may act as a reservoir for measles, causing obstacles to eradication. Furthermore, our model analysis shows that while impactful controls can be achieved by children-focused vaccines, a combined adult-child vaccination program may help assert eradication of the disease.

Effects of vaccination on the two-strain transmission dynamics of COVID-19: Dougherty County, Georgia, USA, as a case study.

The emergence of multiple strains of SARS-COV-2 has made it complicated to predict and control the COVID-19 pandemic. Although some vaccines have been effective in reducing the severity of the disease, these vaccines are designed for a specific strain of the virus and are usually less effective for other strains. In addition, the waning of vaccine-induced immunity, reinfection of recovered people, and incomplete vaccination are challenging to the vaccination program. In this study, we developed a detailed model to describe the multi-strain transmission dynamics of COVID-19 under vaccination. We implemented our model to examine the impact of inter-strain transmission competition under vaccination on the critical outbreak indicators: hospitalized cases, undiagnosed cases, basic reproduction numbers, and the overtake-time by a new strain to the existing strain. In particular, our results on the dependence of the overtake-time on vaccination rates, progression-to-infectious rate, and relative transmission rates provide helpful information for managing a pandemic with circulating two strains. Furthermore, our results suggest that a reduction in the relative transmission rates and a decrease in vaccination dropout rates or an increase in vaccination rates help keep the reproduction number of both strains below unity and keep the number of hospitalized cases and undiagnosed cases at their lowest levels. Moreover, our analysis shows that the second and booster-dose vaccinations are useful for further reducing the reproduction number.

The time distribution of sulfadoxine-pyrimethamine protection from malaria.

Sulfadoxine-pyrimethamine (SP) has been one of the most widely used antimalarial treatments world-wide, and is also used prophylactically in vulnerable populations. In this paper, we develop a mathematical model which allows us to infer the time distribution of SP protection from drug-trial data. Fitting our model to data from a controlled field study in Mali, we find that SP provided protection from malaria for an average of 37.9 days in this pediatric population. We demonstrate that the duration of SP protection is not well described by an exponential distribution, and in fact has a much narrower dispersal about the mean; the best-fit standard deviation predicted by our model was only 17.0 days, as opposed to 41.8 days for the exponential model. We estimate the monthly entomological inoculation rate and the basic reproductive number for malaria in this population, and demonstrate that extremely high SP treatment rates would be necessary to maintain an effective reproductive number below one throughout a single rainy season. These results have implications for further efforts to model the impact of SP treatment, or for investigations of the optimal timing of prophylactic SP.

Effectiveness of alternative semester break schedules on reducing COVID-19 incidence on college campuses.

Despite COVID-19 vaccination programs, the threat of new SARS-CoV-2 strains and continuing pockets of transmission persists. While many U.S. universities replaced their traditional nine-day spring 2021 break with multiple breaks of shorter duration, the effects these schedules have on reducing COVID-19 incidence remains unclear. The main objective of this study is to quantify the impact of alternative break schedules on cumulative COVID-19 incidence on university campuses. Using student mobility data and Monte Carlo simulations of returning infectious student size, we developed a compartmental susceptible-exposed-infectious-asymptomatic-recovered (SEIAR) model to simulate transmission dynamics among university students. As a case study, four alternative spring break schedules were derived from a sample of universities and evaluated. Across alternative multi-break schedules, the median percent reduction of total semester COVID-19 incidence, relative to a traditional nine-day break, ranged from 2 to 4% (for 2% travel destination prevalence) and 8-16% (for 10% travel destination prevalence). The maximum percent reduction from an alternate break schedule was estimated to be 37.6%. Simulation results show that adjusting academic calendars to limit student travel can reduce disease burden. Insights gleaned from our simulations could inform policies regarding appropriate planning of schedules for upcoming semesters upon returning to in-person teaching modalities.

Modeling transmission dynamics of measles in Nepal and its control with monitored vaccination program.

Measles is one of the highly contagious human viral diseases. Despite the availability of vaccines, measles outbreak frequently occurs in many places, including Nepal, partly due to the lack of compliance with vaccination. In this study, we develop a novel transmission dynamics model to evaluate the effects of monitored vaccination programs to control and eliminate measles. We use our model, parameterized with the data from the measles outbreak in Nepal, to calculate the vaccinated reproduction number, $ R_v $, of measles in Nepal. We perform model analyses to establish the global asymptotic stability of the disease-free equilibrium point for $ R_v < 1 $ and the uniform persistence of the disease for $ R_v > 1 $. Moreover, we perform model simulations to identify monitored vaccination strategies for the successful control of measles in Nepal. Our model predicts that the monitored vaccination programs can help control the potential resurgence of the disease.

Insight into Delta variant dominated second wave of COVID-19 in Nepal.

OBJECTIVE: To study the spreading nature of Delta variant (B.1.617.2) dominated COVID-19 in Nepal to help the policymakers assess and manage health care facilities and vaccination programs. METHODS: Deterministic mathematical models in the form of systems of ordinary differential equations were developed to describe the COVID-19 transmission in the high- and the low-risk regions of Nepal. The models were validated using the multiple data sets containing daily new cases in the whole country, the high-risk region, the low-risk region, and cases needing medical care, ICU, and ventilator. RESULTS: We found the reproduction number of Rt=4.2 at the beginning of the second wave, larger than the first wave (∼1.8 estimated previously), indicating that the transmissibility of Delta variant is higher than the wild-type circulated during the first wave. Model predicts that ∼5% of the COVID-19 cases were reported in Nepal, estimating the seroprevalence of ∼63.9% as of July 2021, consistent with the survey conducted by the Government of Nepal. The seroprevalence was expected to reach 94.46% by April 2022, among which ∼46% would have both infection and vaccination. The expected cases from September 2021 to April 2022 is 111,300, among which 11,890 people might need medical care, 3590 need ICU, and 953 need ventilators. The COVID-19 cases and medical care needs could be significantly reduced with proper implementation of vaccination and social distancing. CONCLUSIONS: The data-driven mathematical models are useful to assess control programs in resource-limited countries. The appropriate combination of vaccination and social distancing are necessary to keep the pandemic under-control and manage the medical care facilities in Nepal.

Modeling malaria transmission in Nepal: impact of imported cases through cross-border mobility.

The cross-border mobility of malaria cases poses an obstacle to malaria elimination programmes in many countries, including Nepal. Here, we develop a novel mathematical model to study how the imported malaria cases through the Nepal-India open-border affect the Nepal government's goal of eliminating malaria by 2026. Mathematical analyses and numerical simulations of our model, validated by malaria case data from Nepal, indicate that eliminating malaria from Nepal is possible if strategies promoting the absence of cross-border mobility, complete protection of transmission abroad, or strict border screening and isolation are implemented. For each strategy, we establish the conditions for the elimination of malaria. We further use our model to identify the control strategies that can help maintain a low endemic level. Our results show that the ideal control strategies should be designed according to the average mosquito biting rates that may depend on the location and season.

Viral dynamics during primary simian immunodeficiency virus infection: effect of time-dependent virus infectivity.

A recent experiment involving simian immunodeficiency virus (SIV) infection of macaques revealed that the infectivity of this virus decreased over the first few months of infection. Based on this observation, we introduce a viral dynamic model in which viral infectivity varies over time. The model is fit to viral load data from eight (donor) monkeys infected by intravaginal inoculation of SIVmac251, three monkeys infected by intravenous inoculation of virus isolated from the donors during the ramp-up phase of acute infection, and three monkeys infected by intravenous inoculation of virus isolated at the viral set-point. Although we only analyze data from 14 monkeys, the new model with time-dependent infectivity seems to fit the data significantly better than a widely used model with constant infectivity (P = 2.44 x 10(-11)). Our results indicate that plasma virus infectivity on average decays approximately 8-fold (95% confidence interval [CI] = 5.1 to 10.3) over the course of acute infection, with the decay occurring exponentially with an average rate of 0.28 day(-1) (95% CI = 0.14 to 0.42 day(-1)). The decay rate in set point plasma virus recipient animals is approximately 16 times slower than in ramp-up plasma virus recipient animals and approximately 6 times slower than in donor animals. Throughout acute infection up to the set-point, the infection rate is higher in ramp-up plasma virus recipient animals than in set-point plasma virus recipient animals. These results show that the infectivity depends upon the source of viral infection.

Treatment-mediated alterations in HIV fitness preserve CD4+ T cell counts but have minimal effects on viral load.

For most HIV-infected patients, antiretroviral therapy controls viral replication. However, in some patients drug resistance can cause therapy to fail. Nonetheless, continued therapy with a failing regimen can preserve or even lead to increases in CD4+ T cell counts. To understand the biological basis of these observations, we used mathematical models to explain observations made in patients with drug-resistant HIV treated with enfuvirtide (ENF/T-20), an HIV-1 fusion inhibitor. Due to resistance emergence, ENF was removed from the drug regimen, drug-sensitive virus regrown, and ENF was re-administered. We used our model to study the dynamics of plasma-viral RNA and CD4+ T cell levels, and the competition between drug-sensitive and resistant viruses during therapy interruption and re-administration. Focusing on resistant viruses carrying the V38A mutation in gp41, we found ENF-resistant virus to be 17±3% less fit than ENF-sensitive virus in the absence of the drug, and that the loss of resistant virus during therapy interruption was primarily due to this fitness cost. Using viral dynamic parameters estimated from these patients, we show that although re-administration of ENF cannot suppress viral load, it can, in the presence of resistant virus, increase CD4+ T cell counts, which should yield clinical benefits. This study provides a framework to investigate HIV and T cell dynamics in patients who develop drug resistance to other antiretroviral agents and may help to develop more effective strategies for treatment.