Stochastic modelling of genotypic drug-resistance for human immunodeficiency virus towards long-term combination therapy optimization

Mathematical modeling in perspective of vector-borne viral infections: a review

Background

Viral diseases are highly widespread infections caused by viruses. These viruses are passing from one human to other humans through a certain medium. The medium might be mosquito, animal, reservoir and food, etc. Here, the population of both human and mosquito vectors are important.

Main body of the abstract

The main objectives are here to introduce the historical perspective of mathematical modeling, enable the mathematical modeler to understand the basic mathematical theory behind this and present a systematic review on mathematical modeling for four vector-borne viral diseases using the deterministic approach. Furthermore, we also introduced other mathematical techniques to deal with vector-borne diseases. Mathematical models could help forecast the infectious population of humans and vectors during the outbreak.

Short conclusion

This study will be helpful for mathematical modelers in vector-borne diseases and ready-made material in the review for future advancement in the subject. This study will not only benefit vector-borne conditions but will enable ideas for other illnesses.

SBDiEM: A new mathematical model of infectious disease dynamics

A worldwide multi-scale interplay among a plethora of factors, ranging from micro-pathogens and individual or population interactions to macro-scale environmental, socio-economic and demographic conditions, entails the development of highly sophisticated mathematical models for robust representation of the contagious disease dynamics that would lead to the improvement of current outbreak control strategies and vaccination and prevention policies. Due to the complexity of the underlying interactions, both deterministic and stochastic epidemiological models are built upon incomplete information regarding the infectious network. Hence, rigorous mathematical epidemiology models can be utilized to combat epidemic outbreaks. We introduce a new spatiotemporal approach (SBDiEM) for modeling, forecasting and nowcasting infectious dynamics, particularly in light of recent efforts to establish a global surveillance network for combating pandemics with the use of artificial intelligence. This model can be adjusted to describe past outbreaks as well as COVID-19. Our novel methodology may have important implications for national health systems, international stakeholders and policy makers.

Advances in computational approaches in identifying synergistic drug combinations

Accumulated empirical clinical experience, supported by animal or cell line models, has initiated efforts of predicting synergistic combinatorial drugs with more-than-additive effect compared with the sum of the individual agents. Aiming to construct better computational models, this review started from the latest updated data resources of combinatorial drugs, then summarized the reported mechanism of the known synergistic combinations from aspects of drug molecular and pharmacological patterns, target network properties and compound functional annotation. Based on above, we focused on the main in silico strategies recently published, covering methods of molecular modeling, mathematical simulation, optimization of combinatorial targets and pattern-based statistical/learning model. Future thoughts are also discussed related to the role of natural compounds, drug combination with immunotherapy and management of adverse effects. Overall, with particular emphasis on mechanism of action of drug synergy, this review may serve as a rapid reference to design improved models for combinational drugs.

Determinants of viral load rebound on HIV/AIDS patients receiving antiretroviral therapy: results from South Africa

BACKGROUND

Antiretroviral therapy (ART) has become the standard of care for patients with HIV infection in South Africa and has led to the reduction in AIDS related morbidity and mortality. In developing countries, the nucleosides reverse transcriptase inhibitors (NRTIs) class are widely used because of their low production costs. However patients treated with NRTIs develop varying degree of toxicity after long-term therapy. For this study patients are administered with a triple therapy of two NRTIs and one non-nucleoside reverse transcriptase inhibitor (NNRTI).

METHOD

In this study the progression of HIV in vivo is divided into some viral load states and a continuous time-homogeneous model is fitted to assess the effects of covariates namely gender, age, CD4 baseline, viral load baseline, lactic acidosis, peripheral neuropathy, non-adherence and resistance to treatment on transition intensities between the states. Effects of different drug combinations on transition intensities are also assessed.

RESULTS

The results show no gender differences on transition intensities. The likelihood ratio test shows that the continuous time Markov model for the effects of the covariates including combination give a significantly better fit to the observed data. From almost all states, rates of viral suppression were higher than rates of viral rebound except for patients in state 2 (viral load between 50 and 10,000 copies/mL) where rates of viral rebound to state 3 (viral load between 10,000 and 100,000 copies/mL) were higher than rates of viral suppression to undetectable levels. For this transition, confidence intervals were very small. This was quite notable for patients who were administered with AZT-3TC-LPV/r and FTC-TDF-EFV. Although patients on d4T-3TC-EFV also had higher rates of viral rebound from state 2 than suppression, the difference was not significant.

CONCLUSION

From these findings, we can conclude that administering of any HIV drug regimen is better when based on the viral load level of an HIV+ patient. Before initiation of treatment, patients should be well equipped on how antiretroviral drugs operate including possibilities of toxicity in order to reduce chances of non-adherence to treatment. There should also be a good relationship between patient and health-care-giver to ensure proper adherence to treatment. Uptake of therapy by young patients should be closely monitored by adopting pill counting every time they come for review.

Large-scale inference of conjunctive Bayesian networks

The continuous time conjunctive Bayesian network (CT-CBN) is a graphical model for analyzing the waiting time process of the accumulation of genetic changes (mutations). CT-CBN models have been successfully used in several biological applications such as HIV drug resistance development and genetic progression of cancer. However, current approaches for parameter estimation and network structure learning of CBNs can only deal with a small number of mutations (<20). Here, we address this limitation by presenting an efficient and accurate approximate inference algorithm using a Monte Carlo expectation-maximization algorithm based on importance sampling. The new method can now be used for a large number of mutations, up to one thousand, an increase by two orders of magnitude. In simulation studies, we present the accuracy as well as the running time efficiency of the new inference method and compare it with a MLE method, expectation-maximization, and discrete time CBN model, i.e. a first-order approximation of the CT-CBN model. We also study the application of the new model on HIV drug resistance datasets for the combination therapy with zidovudine plus lamivudine (AZT + 3TC) as well as under no treatment, both extracted from the Swiss HIV Cohort Study database.

AVAILABILITY AND IMPLEMENTATION

The proposed method is implemented as an R package available at https://github.com/cbg-ethz/MC-CBN CONTACT: niko.beerenwinkel@bsse.ethz.ch

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Estimating the dynamics and dependencies of accumulating mutations with applications to HIV drug resistance

We introduce a new model called the observed time conjunctive Bayesian network (OT-CBN) that describes the accumulation of genetic events (mutations) under partial temporal ordering constraints. Unlike other CBN models, the OT-CBN model uses sampling time points of genotypes in addition to genotypes themselves to estimate model parameters. We developed an expectation-maximization algorithm to obtain approximate maximum likelihood estimates by accounting for this additional information. In a simulation study, we show that the OT-CBN model outperforms the continuous time CBN (CT-CBN) (Beerenwinkel and Sullivant, 2009. Markov models for accumulating mutations. Biometrika 96: (3), 645-661), which does not take into account individual sampling times for parameter estimation. We also show superiority of the OT-CBN model on several datasets of HIV drug resistance mutations extracted from the Swiss HIV Cohort Study database.

The individualized genetic barrier predicts treatment response in a large cohort of HIV-1 infected patients

The success of combination antiretroviral therapy is limited by the evolutionary escape dynamics of HIV-1. We used Isotonic Conjunctive Bayesian Networks (I-CBNs), a class of probabilistic graphical models, to describe this process. We employed partial order constraints among viral resistance mutations, which give rise to a limited set of mutational pathways, and we modeled phenotypic drug resistance as monotonically increasing along any escape pathway. Using this model, the individualized genetic barrier (IGB) to each drug is derived as the probability of the virus not acquiring additional mutations that confer resistance. Drug-specific IGBs were combined to obtain the IGB to an entire regimen, which quantifies the virus' genetic potential for developing drug resistance under combination therapy. The IGB was tested as a predictor of therapeutic outcome using between 2,185 and 2,631 treatment change episodes of subtype B infected patients from the Swiss HIV Cohort Study Database, a large observational cohort. Using logistic regression, significant univariate predictors included most of the 18 drugs and single-drug IGBs, the IGB to the entire regimen, the expert rules-based genotypic susceptibility score (GSS), several individual mutations, and the peak viral load before treatment change. In the multivariate analysis, the only genotype-derived variables that remained significantly associated with virological success were GSS and, with 10-fold stronger association, IGB to regimen. When predicting suppression of viral load below 400 cps/ml, IGB outperformed GSS and also improved GSS-containing predictors significantly, but the difference was not significant for suppression below 50 cps/ml. Thus, the IGB to regimen is a novel data-derived predictor of treatment outcome that has potential to improve the interpretation of genotypic drug resistance tests.

Mathematical modeling of infectious disease dynamics

Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host–pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works.