Modelling the effects of adherence to the HIV fusion inhibitor enfuvirtide

Analysis of HIV latent infection model with multiple infection stages and different drug classes

Latently infected CD4+ T cells represent one of the major obstacles to HIV eradication even after receiving prolonged highly active anti-retroviral therapy (HAART). Long-term use of HAART causes the emergence of drug-resistant virus which is then involved in HIV transmission. In this paper, we develop mathematical HIV models with staged disease progression by incorporating entry inhibitor and latently infected cells. We find that entry inhibitor has the same effect as protease inhibitor on the model dynamics and therefore would benefit HIV patients who developed resistance to many of current anti-HIV medications. Numerical simulations illustrate the theoretical results and show that the virus and latently infected cells reach an infected steady state in the absence of treatment and are eliminated under treatment whereas the model including homeostatic proliferation of latently infected cells maintains the virus at low level during suppressive treatment. Therefore, complete cure of HIV needs complete eradication of latent reservoirs.

Global Dynamics of SARS-CoV-2 Infection with Antibody Response and the Impact of Impulsive Drug Therapy

Mathematical modeling is crucial to investigating tthe ongoing coronavirus disease 2019 (COVID-19) pandemic. The primary target area of the SARS-CoV-2 virus is epithelial cells in the human lower respiratory tract. During this viral infection, infected cells can activate innate and adaptive immune responses to viral infection. Immune response in COVID-19 infection can lead to longer recovery time and more severe secondary complications. We formulate a micro-level mathematical model by incorporating a saturation term for SARS-CoV-2-infected epithelial cell loss reliant on infected cell levels. Forward and backward bifurcation between disease-free and endemic equilibrium points have been analyzed. Global stability of both disease-free and endemic equilibrium is provided. We have seen that the disease-free equilibrium is globally stable for R0<1, and endemic equilibrium exists and is globally stable for R0>1. Impulsive application of drug dosing has been applied for the treatment of COVID-19 patients. Additionally, the dynamics of the impulsive system are discussed when a patient takes drug holidays. Numerical simulations support the analytical findings and the dynamical regimes in the systems.

Effect of DAA therapy in hepatitis C treatment - an impulsive control approach

In this article, we have presented a mathematical model to study the dynamics of hepatitis C virus (HCV) disease considering three populations namely the uninfected liver cells, infected liver cells, and HCV with the aim to control the disease. The model possesses two equilibria namely the disease-free steady state and the endemically infected state. There exists a threshold condition (basic reproduction number) that determines the stability of the disease-free equilibrium and the number of the endemic states. We have further introduced impulsive periodic therapy using DAA into the system and studied the efficacy of the DAA therapy for hepatitis C infected patients in terms of a threshold condition. Finally, impulse periodic dosing with varied rate and time interval is adopted for cost effective disease control for finding the proper dose and dosing interval for the control of HCV disease.

A Model for SARS-CoV-2 Infection with Treatment

The current emergence of coronavirus (SARS-CoV-2) puts the world in threat. The structural research on the receptor recognition by SARS-CoV-2 has identified the key interactions between SARS-CoV-2 spike protein and its host (epithelial cell) receptor, also known as angiotensin-converting enzyme 2 (ACE2). It controls both the cross-species and human-to-human transmissions of SARS-CoV-2. In view of this, we propose and analyze a mathematical model for investigating the effect of CTL responses over the viral mutation to control the viral infection when a postinfection immunostimulant drug (pidotimod) is administered at regular intervals. Dynamics of the system with and without impulses have been analyzed using the basic reproduction number. This study shows that the proper dosing interval and drug dose both are important to eradicate the viral infection.

Predicting the long-term impact of voluntary medical male circumcision on HIV incidence among men who have sex with men in Beijing, China

Using a deterministic compartmental modeling procedure to fit prevalence from 2005-2015, we projected new HIV cases during 2016-2026 under different coverage rates ranging from 0.0001 (at baseline) to 0.15 (an optimistic assumption) with simulations on varying transmission rates, model calibration to match historical data, and sensitivity analyses for different assumptions. Compared with the baseline (λ = 0.0001), we found the new HIV cases would reduce with the increase of coverage rates of the voluntary medical male circumcision (VMMC) among men who have sex wtih men (MSM). The higher the coverage rate, the lower the new HIV incidence would be. As one of the first studies to model the potential impact of VMMC among MSM in China, our model suggested a modest to the significant public health impact of VMMC. Even at just 15% VMMC annual uptake rate, the reduction in new infections is substantial. Therefore, there is a strong need to determine the efficacy of VMMC among MSM, to improve the evidence base for its potential use among MSM in low circumcision settings. Only then can policymakers decide whether to incorporate VMMC into a package of HIV prevention interventions targeting MSM.

Modeling economic and epidemiological impact of voluntary medical male circumcision among men who have sex with men in Beijing, China

Voluntary medical male circumcision (VMMC) among men who have sex with men (MSM) may protect against HIV acquisition. We conducted a series of analyses to assess if expanded VMMC might reduce HIV incidence among MSM effectively and economically. We used a deterministic compartmental model to project new HIV cases (2016-2026) under annual VMMC coverage rates (λ) ranging from 0.0001 to 0.15. The 'number needed to avert' (NNA) is defined as the cumulative number of VMMCs conducted up to that year divided by the cumulative number of HIV cases averted in that specific year. Compared with the baseline circumcision coverage rate, we projected that new HIV cases would be reduced with increasing coverage. By 2026 (last year simulated), the model generated the lowest ratio (11.10) when the annual circumcision rate was the most optimistic (λ = 0.15). The breakeven point was observed at the year of 2019 with the annual VMMC coverage rate of 0.001. The total cost saved by averting HIV cases would range from 2.5 to 811 million US dollars by the end of 2026 with different hypothetical coverage rates. Our model suggests that acceleration in VMMC implementation among MSM could help stem the HIV/AIDS epidemic.

Modeling of fusion inhibitor treatment of RSV in African green monkeys

Respiratory syncytial virus (RSV) is a respiratory infection that can cause serious illness, particularly in infants. In this study, we test four different model implementations for the effect of a fusion inhibitor, including one model that combines different drug effects, by fitting the models to data from a study of TMC353121 in African green monkeys. We use mathematical modeling to estimate the drug efficacy parameters, ε_max, the maximum efficacy of the drug, and EC₅₀, the drug concentration needed to achieve half the maximum effect. We find that if TMC353121 is having multiple effects on viral kinetics, more detailed data, using different treatment delays, is needed to detect this effect.

The effect of vaccination to dendritic cell and immune cell interaction in HIV disease progression

In this research paper, our main objective is to find out the meticulous role of activated dendritic cells (DCs) during the human immunodeficiency virus (HIV) infection process. DCs play a dual role by enhancing both HIV infection progression, as well as antiviral immune response. To explore the implications of these dual roles, we have formulated our mathematical model and analyzed the model by both analytical and numerical approaches. By using an impulsive differential equation, we have studied the effect of DC-based vaccination. Analytically we have determined the threshold value of drug dosage and dosing interval for optimum levels of infection. We have also investigated the effect of perfect adherence of drug dose on the immune cell count in extreme cases and observed that, systematic drug dose of the immune cells leads to its maximum level.

Toward modular biological models: defining analog modules based on referent physiological mechanisms

Background

Currently, most biomedical models exist in isolation. It is often difficult to reuse or integrate models or their components, in part because they are not modular. Modular components allow the modeler to think more deeply about the role of the model and to more completely address a modeling project’s requirements. In particular, modularity facilitates component reuse and model integration for models with different use cases, including the ability to exchange modules during or between simulations. The heterogeneous nature of biology and vast range of wet-lab experimental platforms call for modular models designed to satisfy a variety of use cases. We argue that software analogs of biological mechanisms are reasonable candidates for modularization. Biomimetic software mechanisms comprised of physiomimetic mechanism modules offer benefits that are unique or especially important to multi-scale, biomedical modeling and simulation.

Results

We present a general, scientific method of modularizing mechanisms into reusable software components that we call physiomimetic mechanism modules (PMMs). PMMs utilize parametric containers that partition and expose state information into physiologically meaningful groupings. To demonstrate, we modularize four pharmacodynamic response mechanisms adapted from an in silico liver (ISL). We verified the modularization process by showing that drug clearance results from in silico experiments are identical before and after modularization. The modularized ISL achieves validation targets drawn from propranolol outflow profile data. In addition, an in silico hepatocyte culture (ISHC) is created. The ISHC uses the same PMMs and required no refactoring. The ISHC achieves validation targets drawn from propranolol intrinsic clearance data exhibiting considerable between-lab variability. The data used as validation targets for PMMs originate from both in vitro to in vivo experiments exhibiting large fold differences in time scale.

Conclusions

This report demonstrates the feasibility of PMMs and their usefulness across multiple model use cases. The pharmacodynamic response module developed here is robust to changes in model context and flexible in its ability to achieve validation targets in the face of considerable experimental uncertainty. Adopting the modularization methods presented here is expected to facilitate model reuse and integration, thereby accelerating the pace of biomedical research.

Resistance to protease inhibitors in a model of HIV-1 infection with impulsive drug effects

BACKGROUND

The emergence of drug resistance is one of the most prevalent reasons for treatment failure in HIV therapy. This has severe implications for the cost of treatment, survival and quality of life.

METHODS

We use mathematical modelling to describe the interaction between T cells, HIV-1 and protease inhibitors. We use impulsive differential equations to examine the effects of different levels of protease inhibitors in a T cell. We classify three different regimes according to whether the drug efficacy is low, intermediate or high. The model includes two strains: the wild-type strain, which initially dominates in the absence of drugs, and the mutant strain, which is the less efficient competitor, but has more resistance to the drugs.

RESULTS

Drug regimes may take trajectories through one, two or all three regimes, depending on the dosage and the dosing schedule. Stability analysis shows that resistance does not emerge at low drug levels. At intermediate drug levels, drug resistance is guaranteed to emerge. At high drug levels, either the drug-resistant strain will dominate or, in the absence of longer-lived reservoirs of infected cells, a region exists where viral elimination could theoretically occur. We provide estimates of a range of dosages and dosing schedules where the trajectories lie either solely within a region or cross multiple regions.

CONCLUSION

Under specific circumstances, if the drug level is physiologically tolerable, elimination of free virus is theoretically possible. This forms the basis for theoretical control using combination therapy and for understanding the effects of partial adherence.