Population-based Mathematical Models Research Articles

Modeling the Impacts of Diagnosis and Treatment of Snakebite Envenoming Victims with Anti-Snake Venom in a Community

Snakebite envenoming (SBE) is one of the major causes of deaths and disabilities in tropical and subtropical countries especially in the continents of Asia and Africa. Report revealed that on average, 5-8 and about 3,000 cases of SBE are recorded daily and yearly respectively in northeast Nigeria which population are largely agriculturists. Thus, snakebite (SB) led to economy setback and slows down productivity among the workforce as a result of disabilities induced by SBE. Consequently, the revenue generation even including income facing declined. This paper proposes population-based mathematical model for studying the dynamic impacts of diagnosis and treatment of snakebite envenoming victims with anti-snake venom in a community. The model is rigorously analyzed using relevant techniques and theorems in dynamical systems. The model was validated using monthly reported data on snakebite envenoming from 2020–2022, collected from snakebite treatment and research hospital (STRH) Kaltungo in northeast Nigeria. The qualitative study revealed that the model has snakebite-envenoming-free and snakebite-envenoming-endemic equilibrium points. It is shown via the Lyapunov function in conjunction with the Lassale invariance principle that these two equilibrium points are globally asymptotically stable. Furthermore, numerical simulations of the model were carried out to investigate the impact of the diagnosis of snakebite envenoming victims and the treatment of the same on the burden of snakebite envenoming. The results of the simulations revealed that appropriate diagnosis and treatment of snakebite envenoming victims with anti-snake venom could significantly reduce the number of snakebite-induced deaths and disabilities. This work can serve as a framework for making policy and decision in addressing the issues of SBE in the public healthcares in the study region and beyond.

Epidemiological impact of public health interventions against diabetes in Qatar: mathematical modeling analyses.

To predict the epidemiological impact of specific, and primarily structural public health interventions that address lifestyle, dietary, and commuting behaviors of Qataris as well as subsidies and legislation to reduce type 2 diabetes mellitus (T2DM) burden among Qataris. A deterministic population-based mathematical model was used to investigate the impact of public health interventions on the epidemiology of T2DM among Qataris aged 20-79 years, which is the age range typically used by the International Diabetes Federation for adults. The study evaluated the impact of interventions up to 2050, a three-decade time horizon, to allow for the long-term effects of different types of interventions to materialize. The impact of each intervention was evaluated by comparing the predicted T2DM incidence and prevalence with the intervention to a counterfactual scenario without intervention. The model was parameterized using representative data and stratified by sex, age, T2DM risk factors, T2DM status, and intervention status. All intervention scenarios had an appreciable impact on reducing T2DM incidence and prevalence. A lifestyle management intervention approach, specifically applied to those who are categorized as obese and ≥35 years old, averted 9.5% of new T2DM cases by 2050. An active commuting intervention approach, specifically increasing cycling and walking, averted 8.5% of new T2DM cases by 2050. Enhancing consumption of healthy diets including fruits and vegetables, specifically a workplace intervention involving dietary modifications and an educational intervention, averted 23.2% of new T2DM cases by 2050. A subsidy and legislative intervention approach, implementing subsidies on fruits and vegetables and taxation on sugar-sweetened beverages, averted 7.4% of new T2DM cases by 2050. A least to most optimistic combination of interventions averted 22.8-46.9% of new T2DM cases by 2050, respectively. Implementing a combination of individual-level and structural public health interventions is critical to prevent T2DM onset and to slow the growing T2DM epidemic in Qatar.

Cost-effectiveness Analysis of a Personalized, Teleretinal-Inclusive Screening Policy for Diabetic Retinopathy via Markov Modeling

Although teleretinal imaging has proved effective in increasing population-level screening for diabetic retinopathy (DR), there is a lack of quantitative understanding of how to incorporate teleretinal imaging into existing screening guidelines. We develop a mathematical model to determine personalized DR screening recommendations that utilize teleretinal imaging and evaluate the cost-effectiveness of the personalized screening policy. A partially observable Markov decision process is employed to determine personalized screening recommendations based on patient compliance, willingness to pay, and A1C level. Deterministic sensitivity analysis was conducted to evaluate the impact of patient-specific factors on personalized screening policy. The cost-effectiveness of identified screening policies was evaluated via hidden-Markov chain Monte Carlo simulation on a data-based hypothetical cohort. Screening policies were simulated for a hypothetical cohort of 500 000 patients with parameters based on the literature and electronic medical records of 2457 patients who received teleretinal imaging from 2013 to 2020 from the Harris Health System. Population-based mathematical modeling study. Interventions included dilated fundus examinations referred to as clinical screening, teleretinal imaging, and wait and watch recommendations. Personalized screening recommendations based on patient-specific factors. Accumulated quality-adjusted life-years (QALYs) and cost (USD) per patient under different screening policies. Incremental cost-effectiveness ratio to compare different policies. For the base cohort, on average, teleretinal imaging was recommended 86.7% of the time over each patient's lifetime. The model-based personalized policy dominated other standardized policies, generating more QALY gains and cost savings for at least 57% of the base cohort. Similar outcomes were observed in sensitivity analyses of the base cohort and the Harris Health-specific cohort and rural population scenario analysis. A mathematical model was developed as a decision support tool to identify a personalized screening policy that incorporates both teleretinal imaging and clinical screening and adapts to patient characteristics. Compared with current standardized policies, the model-based policy significantly reduces costs, whereas it is performing comparably, if not better, in terms of QALY gain. A personalized approach to DR screening has significant potential benefits that warrant further exploration. Proprietary or commercial disclosure may be found after the references.

Cohort profile: The Chikwawa lung health cohort; a population-based observational non-communicable respiratory disease study of adults in Malawi.

The aim of this article is to provide a detailed description of the Chikwawa lung health cohort which was established in rural Malawi to prospectively determine the prevalence and causes of lung disease amongst the general population of adults living in a low-income rural setting in Sub-Saharan Africa. A total of 1481 participants were randomly identified and recruited in 2014 for the baseline study. We collected data on demographic, socio-economic status, respiratory symptoms and potentially relevant exposures such as smoking, household fuels, environmental exposures, occupational history/exposures, dietary intake, healthcare utilization, cost (medication, outpatient visits and inpatient admissions) and productivity losses. Spirometry was performed to assess lung function. At baseline, 56.9% of the participants were female, mean age was 43.8 (SD:17.8) and mean body mass index (BMI) was 21.6 Kg/m2 (SD: 3.46). The cohort has reported the prevalence of chronic respiratory symptoms (13.6%, 95% confidence interval [CI], 11.9-15.4), spirometric obstruction (8.7%, 95% CI, 7.0-10.7), and spirometric restriction (34.8%, 95% CI, 31.7-38.0). Additionally, an annual decline in forced expiratory volume in one second [FEV1] of 30.9mL/year (95% CI: 21.6 to 40.1) and forced vital capacity [FVC] by 38.3 mL/year (95% CI: 28.5 to 48.1) has been reported. The ongoing phases of follow-up will determine the annual rate of decline in lung function as measured through spirometry and the development of airflow obstruction and restriction, and relate these to morbidity, mortality and economic cost of airflow obstruction and restriction. Population-based mathematical models will be developed driven by the empirical data from the cohort and national population data for Malawi to assess the effects of interventions and programmes to address the lung burden in Malawi. The present follow-up study started in 2019.

Does infection with Chlamydia trachomatis induce long-lasting partial immunity? Insights from mathematical modelling

ObjectivesTo explore whether existence of long-lasting partial immunity against reinfection with Chlamydia trachomatis is necessary to explain C. trachomatis prevalence patterns by age and sexual risk, and to provide a...

A Comparative Analysis of Parameter Estimation Strategies for Mathematical Modeling of Ion Channel Gating

Mathematical modeling in cardiac electrophysiology is well established; however, the veracity of model predictions for pharmacological design and testing is unclear. Ion channel gating is often modeled with Markov schemes that reflect different occupancy states of the channel. Although experimental data are always used to constrain the parameters of these models, it often remains unclear whether a set of parameter values is unique, or whether alternative parameter sets could fit the data equally well. Here we have compared alternative parameter estimation strategies to build a patient-specific approach to in-silico drug testing. Using a published Markov representation of the cardiac Na+ channel, we aimed to optimize the value of rate constants regulating the channel's transition between different states. Data derived from voltage-clamp experiments, performed by implementing a traditional voltage square steps protocol in HEK293 cells, were used to test the following approaches: (1) “broad fitting algorithm” using population-based mathematical modeling; (2) optimization through genetic algorithm; and (3) optimization through direct search simplex algorithm. We generated a population (n=10000) of channel variants by randomizing Markov model rate constants and used it to replicate the electrophysiology results. While approaches (2) and (3) identify a single solution that matches the experimental findings, approach (1) provided a population (n=48) of channel variants that reproduce distinctive features of experimental activation and inactivation curves. We conclude that adopting a population-based strategy allows us to find several parameter sets that are all compatible with experimental results and cannot be captured by other common optimization strategies. These solutions recreate the level of experimental variability and account for the fact that different rate constants can compensate for one another. Evaluation of the three algorithms on action potential clamp and dynamic clamp experiments is currently ongoing.

Population-Based Mathematical Model of Solid-State Deracemization via Temperature Cycles

Recently, temperature cycles have been shown to lead to total deracemization of conglomerate forming compounds, in the presence of a racemizing agent. Even though several experimental studies have ...

Implications of population-level immunity for the emergence of artemisinin-resistant malaria: a mathematical model

BackgroundArtemisinin-resistant Plasmodium falciparum has emerged in the Greater Mekong Subregion, an area of relatively low transmission, but has yet to be reported in Africa. A population-based mathematical model was used to investigate the relationship between P. falciparum prevalence, exposure-acquired immunity and time-to-emergence of artemisinin resistance. The possible implication for the emergence of resistance across Africa was assessed.MethodsThe model included human and mosquito populations, two strains of malaria (“wild-type”, “mutant”), three levels of human exposure-acquired immunity (none, low, high) with two types of immunity for each level (sporozoite/liver stage immunity and blood-stage/gametocyte immunity) and drug pressure based on per-capita treatment numbers.ResultsThe model predicted that artemisinin-resistant strains may circulate up to 10 years longer in high compared to low P. falciparum prevalence areas before resistance is confirmed. Decreased time-to-resistance in low prevalence areas was explained by low genetic diversity and immunity, which resulted in increased probability of selection and spread of artemisinin-resistant strains. Artemisinin resistance was estimated to be established by 2020 in areas of Africa with low (< 10%) P. falciparum prevalence, but not for 5 or 10 years later in moderate (10–25%) or high (> 25%) prevalence areas, respectively.ConclusionsAreas of low transmission and low immunity give rise to a more rapid expansion of artemisinin-resistant parasites, corroborating historical observations of anti-malarial resistance emergence. Populations where control strategies are in place that reduce malaria transmission, and hence immunity, may be prone to a rapid emergence and spread of artemisinin-resistant strains and thus should be carefully monitored.

Population-based mathematical modeling antihypertensive drugs effect using BioUML platform

Population-based mathematical modeling antihypertensive drugs effect using BioUML platform

Population-Based Mathematical Modeling to Deduce Disease-Causing Cardiac Na+ Channel Gating Defects

Mutations in the SCN5A gene, which encodes the primary cardiac Na+ channel (Nav1.5), can cause arrhythmic disorders such as Type 3 Long QT Syndrome (LQT3). A pediatric patient with severe ventricular arrhythmias was recently determined to carry a missense mutation in SCN5A that putatively leads to a replacement of glutamine by proline at residue 1475 (Q1475P). We sought to uncover, through population-based mathematical modeling of ion channel gating: (1) what defects in gating at the molecular level could account for cellular electrophysiological recordings; and (2) whether these alterations to channel gating could reproduce the patient's LQT3 phenotype. Electrophysiology experiments, performed in HEK293 cells, demonstrated that, compared with Wild Type (WT) Nav1.5 channels, Q1475P channels exhibited: (1) a positive shift in the activation curve; (2) a positive shift in the inactivation curve; (3) faster inactivation; and (4) faster recovery from inactivation. Simulations attempted to recapitulate these results by randomizing parameters in a published Markov model of Nav1.5 gating, generating a large (n=10,000) population of channel variants, filtering to match WT and Q1475P channel behaviors. This produced subpopulations of channel variants describing the gating of either genotype. The analysis suggested that the channel gating steps most likely to be affected by the mutation include transitions from: (1) open to closed, (2) inactivated to closed; and (3) closed to inactivated. In addition, when simulated Nav1.5 channels were incorporated into a model of the human ventricular action potential, Q1475P channels were more likely than WT channels to produce arrhythmogenic early afterdepolarizations (EADs). The results provide important insight into this patient's LQT3 phenotype and demonstrate how population-based modeling can generate mechanistic hypotheses about alterations in ion channel gating that result from mutations.

Prediction of flu epidemic peaks in st. petersburg through population-based mathematical models

Prediction of flu epidemic peaks in st. petersburg through population-based mathematical models

Projecting the epidemiological effect, cost-effectiveness and transmission of HIV drug resistance in Vietnam associated with viral load monitoring strategies.

The objective of this study was to investigate the potential epidemiological impact of viral load (VL) monitoring and its cost-effectiveness in Vietnam, where transmitted HIV drug resistance (TDR) prevalence has increased from <5% to 5%-15% in the past decade. Using a population-based mathematical model driven by data from Vietnam, we simulated scenarios of various combinations of VL testing coverage, VL thresholds for second-line ART initiation and availability of HIV drug-resistance tests. We assessed the cost per disability-adjusted life year (DALY) averted for each scenario. Projecting expected ART scale-up levels, to approximately double the number of people on ART by 2030, will lead to an estimated 18 510 cases (95% CI: 9120-34 600 cases) of TDR and 55 180 cases (95% CI: 40 540-65 900 cases) of acquired drug resistance (ADR) in the absence of VL monitoring. This projection corresponds to a TDR prevalence of 16% (95% CI: 11%-24%) and ADR of 18% (95% CI: 15%-20%). Annual or biennial VL monitoring with 30% coverage is expected to relieve 12%-31% of TDR (2260-5860 cases), 25%-59% of ADR (9620-22 650 cases), 2%-6% of HIV-related deaths (360-880 cases) and 19 270-51 400 DALYs during 2015-30. The 30% coverage of VL monitoring is estimated to cost US$4848-5154 per DALY averted. The projected additional cost for implementing this strategy is US$105-268 million over 2015-30. Our study suggests that a programmatically achievable 30% coverage of VL monitoring can have considerable benefits for individuals and leads to population health benefits by reducing the overall national burden of HIV drug resistance. It is marginally cost-effective according to common willingness-to-pay thresholds.

Population-Based Mathematical Modeling Facilitates the Interpretation of Dynamic Clamp Experiments in Cardiomyocytes

Dynamic clamp (DC) is a powerful method that comprehensively probes how the AP responds to perturbations based on different currents intrinsic to cardiomyocytes. In this closed-loop method, a current is calculated based on the time course of measured voltage, and a scaled version of the calculated current is applied to the cell in real-time. However, since DC currents differ from endogenous currents in several ways, care needs to be taken in interpreting results of these experiments. Since our experiments found significant between-cell heterogeneity in the response to DC perturbations, in order to guide appropriate understanding of these experiments we performed population-based simulations of DC perturbations with different assumptions that reflect how DC currents differ from endogenous currents.DC currents lack the ionic selectivity of endogenous currents. Simulations of DC perturbations with and without ionic selectivity showed that a lack of ionic selectivity leads to overestimation of the effect of the L-type calcium current on APD, but that the effects of other perturbations were largely unaffected. Furthermore, while endogenous currents respond directly to intracellular ionic concentrations, these values are unknown in experiments and must instead be estimated for the calculation of DC currents. We performed simulations where DC currents were calculated using either true ionic concentrations or estimates thereof, and while we found only minor differences in the mean perturbation effect sizes between these two paradigms, the patterns of variability in cell response across a population of models differed significantly, with the latter method producing a closer approximation of experimental results.By illustrating the strengths and shortcomings of how well dynamic clamp perturbations approximate changes in endogenous currents, these simulations allow for more accurate interpretation of dynamic clamp results.

There and back again: Iterating between population-based modeling and experiments reveals surprising regulation of calcium transients in rat cardiac myocytes

While many ion channels and transporters involved in cardiac cellular physiology have been identified and described, the relative importance of each in determining emergent cellular behaviors remains unclear. Here we address this issue with a novel approach that combines population-based mathematical modeling with experimental tests to systematically quantify the relative contributions of different ion channels and transporters to the amplitude of the cellular Ca2+ transient. Sensitivity analysis of a mathematical model of the rat ventricular cardiomyocyte quantified the response of cell behaviors to changes in the level of each ion channel and transporter, and experimental tests of these predictions were performed to validate or invalidate the predictions. The model analysis found that partial inhibition of the transient outward current in rat ventricular epicardial myocytes was predicted to have a greater impact on Ca2+ transient amplitude than either: (1) inhibition of the same current in endocardial myocytes, or (2) comparable inhibition of the sarco/endoplasmic reticulum Ca2+ ATPase (SERCA). Experimental tests confirmed the model predictions qualitatively but showed some quantitative disagreement. This guided us to recalibrate the model by adjusting the relative importance of several Ca2+ fluxes, thereby improving the consistency with experimental data and producing a more predictive model. Analysis of human cardiomyocyte models suggests that the relative importance of outward currents to Ca2+ transporters is generalizable to human atrial cardiomyocytes, but not ventricular cardiomyocytes. Overall, our novel approach of combining population-based mathematical modeling with experimental tests has yielded new insight into the relative importance of different determinants of cell behavior.

Comprehensive Analysis of Behavioral Variability in Real and Simulated Populations of Rabbit Left Ventricular Cardiomyocytes

Variability in behavior between cells and individuals is an important yet poorly studied phenomenon. Studies of cardiac physiology generally focus on typical behavior rather than quantitatively examining variability, and the causes and implications of behavioral variability in these systems are largely unknown. One reason for this is that the low-throughput nature of most physiology experiments makes studies of variability a daunting challenge. We implement two complementary approaches to overcome this: population-based mathematical modeling and higher-throughput experimental methods.We have applied population-based modeling approaches to two models of electrophysiology and calcium handling in the rabbit LV cardiomyocyte, creating a population of cells by varying parameters representing levels of ion channels and transporters. This analysis reveals several key features of behavioral variability in these populations, including: (i) the same population shows much greater variability in calcium transient (CaT) amplitude than in action potential duration (APD), indicating a potentially fundamental propensity for variability in CaTs, (ii) covariation occurs between outputs (e.g. positive correlations between CaT duration and APD) and enables prediction of the effects of some perturbations (e.g. partial block of L-type current) based on baseline behaviors.This theoretical analysis is complemented with experimental measurements of variability using the recently-developed CellOPTIQ system, which allows repeat optical measurements of APs and CaTs to be made with increased throughput (up to 100 cells in 2-3 hours). Early measurements of APD50 from cells isolated from the LV of a single rabbit (n=85 cells) show an approximately normal distribution (mean=297 ms, SD=46 ms, range 151-445 ms), with cells from other rabbits showing similar distributions. These experimental measurements allow for comprehensive quantification of variability and testing of hypotheses generated by model analysis (e.g. correlations between outputs and different degrees of variability between outputs).

Real-time influenza forecasts during the 2012–2013 season

Recently, we developed a seasonal influenza prediction system that uses an advanced data assimilation technique and real-time estimates of influenza incidence to optimize and initialize a population-based mathematical model of influenza transmission dynamics. This system was used to generate and evaluate retrospective forecasts of influenza peak timing in New York City. Here we present weekly forecasts of seasonal influenza developed and run in real time for 108 cites in the United States during the recent 2012–2013 season. Reliable ensemble forecasts of influenza outbreak peak timing with leads of up to 9 weeks were produced. Forecast accuracy increased as the season progressed, and the forecasts significantly outperformed alternate, analog prediction methods. By Week 52, prior to peak for the majority of cities, 63% of all ensemble forecasts were accurate. To our knowledge, this is the first time predictions of seasonal influenza have been made in real time and with demonstrated accuracy.

Pharmacodynamics of Vancomycin at Simulated Epithelial Lining Fluid Concentrations against Methicillin-Resistant Staphylococcus aureus (MRSA): Implications for Dosing in MRSA Pneumonia

Little is known regarding killing activity of vancomycin against methicillin (meticillin)-resistant Staphylococcus aureus (MRSA) in pneumonia since the extent of vancomycin penetration into epithelial lining fluid (ELF) has not been definitively established. We evaluated the impact of the extent of ELF penetration on bacterial killing and resistance by simulating a range of vancomycin exposures (24-h free drug area under the concentration-time curve [fAUC24]/MIC) using an in vitro pharmacodynamic model and population-based mathematical modeling. A high-dose, 1.5-g-every-12-h vancomycin regimen according to American Thoracic Society/Infectious Diseases Society of America guidelines (trough concentration, 15 mg/liter) with simulated ELF/plasma penetration of 0, 20, 40, 60, 80, or 100% (fAUC24/MIC of 0, 70, 140, 210, 280, or 350) was evaluated against two agr-functional, group II MRSA clinical isolates obtained from patients with a bloodstream infection (MIC = 1.0 mg/liter) at a high inoculum of 10(8) CFU/ml. Despite high vancomycin exposures and 100% penetration, all regimens up to a fAUC24/MIC of 350 did not achieve bactericidal activity. At regimens of < or = 60% penetration (fAUC24/MIC < or = 210), stasis and regrowth occurred, amplifying the development of intermediately resistant subpopulations. Regimens simulating > or = 80% penetration (fAUC24/MIC > or = 280) suppressed development of resistance. Resistant mutants amplified by suboptimal vancomycin exposure displayed reduced rates of autolysis (Triton X-100) at 72 h. Bacterial growth and death were well characterized by a Hill-type model (r2 > or = 0.984) and a population pharmacodynamic model with a resistant and susceptible subpopulation (r2 > or = 0.965). Due to the emergence of vancomycin-intermediate resistance at a fAUC24/MIC of < or = 210, exceeding this exposure breakpoint in ELF may help to guide optimal dosage regimens in the treatment of MRSA pneumonia.

Dense gap-junction connections support dynamic Turing structures in the cortex

The recent report by Fukuda et al [1] provides convincing evidence for dense gap-junction connectivity between inhibitory neurons in the cat visual cortex, each neuron making 60 +/- 12 gap-junction dendritic connections with neurons in both the same and adjoining orientation columns. These resistive connections provide a source of diffusive current to the receiving neuron, supplementing the chemical-synaptic currents generated by incoming action-potential spike activity. Fukuda et al describe how the gap junctions form a dense and homogeneous electrical coupling of interneurons, and propose that this diffusion-coupled network provides the substrate for synchronization of neuronal populations. To date, large-scale population-based mathematical models of the cortex have ignored diffusive communication between neurons. Here we augment a well-established mean-field cortical model [2] by incorporating gap-junction-mediated diffusion currents, and we investigate the implications of strong diffusive coupling. The significant result is the model prediction that the 2D cortex can spontaneously generate centimetre-scale Turing structures (spatial patterns), in which regions of high-firing activity are intermixed with regions of low-firing activity (see Fig. ​Fig.1).1). Since coupling strength decreases with increases in firing rate, these patterns are expected to exchange contrast on a slow time-scale, with low-firing patches increasing their activity at the expense of high-firing patches. These theoretical predictions are consistent with the slowly fluctuating large-scale brain-activity images detected from the BOLD (blood oxygen-level-dependent) signal [3]. Figure 1 Diffusion-induced Turing patterns in a square cortex of side 25 cm. Panel a shows the case of zero diffusion: the cortex organizes into a diffuse, cloud-like pattern, but fails to generate a Turing structure. Panels b-d show increasing inhibitory diffusion. ...

Population-based mathematical modeling (PBMM) of institutional cesarean section rates

Cesarean section (CS) rates are typically based on raw data, without consideration of the obstetric population. A government agency recently described our hospital as having the highest regional CS rate. Our objective was to develop a PBMM to adjust our CS rate.