A Coupled Spatial-Network Model: A Mathematical Framework for Applications in Epidemiology.

There is extensive evidence that network structure (e.g., air transport, rivers, or roads) may significantly enhance the spread of epidemics into the surrounding geographical area. A new compartmental modeling framework is proposed which couples well-mixed (ODE in time) population centers at the vertices, 1D travel routes on the graph's edges, and a 2D continuum containing the rest of the population to simulate how an infection spreads through a population. The edge equations are coupled to the vertex ODEs through junction conditions, while the domain equations are coupled to the edges through boundary conditions. A numerical method based on spatial finite differences for the edges and finite elements in the 2D domain is described to approximate the model, and numerical verification of the method is provided. The model is illustrated on two simple and one complex example geometries, and a parameter study example is performed. The observed solutions exhibit exponential decay after a certain time has passed, and the cumulative infected population over the vertices, edges, and domain tends to a constant in time but varying in space, i.e., a steady state solution.

Sir Robert Edwards: from the science of human conception to the reality of IVF birth.

With a new Netflix film Joy telling the dramatic story of IVF, Dr Kamal Ahuja recalls the inspirational role that the late Sir Robert Edwards played in his own career and in the foundation of the London Women's Clinic.

Optimal control for an SIR model with limited hospitalised patients.

This paper analyses the optimal control of infectious disease propagation using a classic susceptible-infected-recovered (SIR) model characterised by permanent immunity and the absence of available vaccines. The control is performed over a time-dependent mean reproduction number, in order to minimise the cumulative number of ever-infected individuals (recovered), under different constraints. We consider constraints on non-pharmaceutical interventions ranging from partial lockdown to non-intervention, as well as the social and economic costs associated with such interventions, and the capacity limitations of intensive care units that limits the number of infected individuals to a maximum allowed value. We rigorously derive an optimal quarantine strategy based on necessary optimality conditions. The obtained optimal strategy is of a boundary-bang type, comprising three phases: an initial phase with no intervention, a second phase maintaining the infected population at its maximum possible value, and a final phase of partial lockdown applied over a single interval. The optimal policy is further refined by optimising the transition times between these phases. We show that these results are in excellent agreement with the numerical solution of the problem.

Modeling tuberculosis transmission dynamics in Kazakhstan using SARIMA and SIR models.

Tuberculosis (TB) is a highly contagious disease that remains a global concern affecting numerous countries. Kazakhstan has been facing considerable challenges in TB prevention and treatment for decades. This study aims to understand TB transmission dynamics by developing and comparing statistical and deterministic models: Seasonal Autoregressive Integrated Moving Average (SARIMA) and the basic Susceptible-Infected-Recovered (SIR). TB data from 2014 to 2019 were collected from the Unified National Electronic Health System (UNEHS) using retrospective quantitative analysis. SARIMA models were able to capture seasonal variations, with Model 2 exhibiting superior predictive accuracy. Both models showed declining TB incidence and revealed a notable predictive performance evaluated by statistical metrics. In addition, the SIR model calculated the basic reproduction number ([Formula: see text]) below 1, indicating a receding epidemic. Models proved the capability of each to accurately capture trends (SARIMA) and provide mathematical insights (SIR) into TB transmission dynamics. This study contributes to the general knowledge of TB transmission dynamics in Kazakhstan thus laying the foundation for more comprehensive studies on TB and control strategies.

A combined neural ODE-Bayesian optimization approach to resolve dynamics and estimate parameters for a modified SIR model with immune memory.

We propose a novel hybrid approach that integrates Neural Ordinary Differential Equations (NODEs) with Bayesian optimization to address the dynamics and parameter estimation of a modified time-delay-type Susceptible-Infected-Removed (SIR) model incorporating immune memory. This approach leverages a neural network to produce continuous multi-wave infection profiles by learning from both data and the model. The time-delay component of the SIR model, expressed through a convolutional integral, results in an integro-differential equation. To resolve these dynamics, we extend the NODE framework, employing a Runge-Kutta solver, to handle the challenging convolution integral, enabling us to fit the data and learn the parameters and dynamics of the model. Additionally, through Bayesian optimization, we enhance prediction accuracy while focusing on long-term dynamics. Our model, applied to COVID-19 data from Mexico, South Africa, and South Korea, effectively learns critical time-dependent parameters and provides accurate short- and long-term predictions. This combined methodology allows for early prediction of infection peaks, offering significant lead time for public health responses.

Solutions to SIR/SEIR epidemic models with exponential series: Numerical and non numerical approaches.

This study revisits the mathematical SIR/SEIR epidemic models, aiming to introduce novel exponential-type series solutions. Beyond standard non-dimensionalization, we implement a successful rescaling technique that reduces the parameter count in classical epidemiology. Consequently, solutions for the SIR model are determined solely by the basic reproduction number and initial infected fractions. Similarly, the SEIR model requires only the transmission-to-recovery ratio and initial exposed fractions. We present both numerical and non numerical solutions, alongside elucidating the limitations on the existence of exponential-type series solutions. Our analysis reveals that these solutions are valid under two key conditions: endemic situations and early epidemic stages, where the basic reproduction number is close to one. We graphically illustrate the range of physical parameters guaranteeing the existence of non numerical exponential series solutions. However, for epidemic/pandemic outbreaks with significantly higher reproduction numbers, achieving complete convergence of the exponential series across the entire physical domain becomes impossible. In such cases, we divide the exponential series solution into two zones: from initial time to peak time and from peak time to the final epidemic time. For the first zone, where convergence is slow, we successfully employ Padé approximants to accelerate the convergence of the series. This accelerated solution is then smoothly joined to the second zone solution once the peak time is identified within the first region. The presented non numerical solutions are envisioned to serve as valuable benchmarks for testing and enhancing other numerical approaches used to solve epidemic models and their variants.

Application and Significance of SIRVB Model in Analyzing COVID-19 Dynamics.

In the summer of 2024, COVID-19 positive cases spiked in many countries, but it is no longer a deadly pandemic thanks to global herd immunity to the SARS-CoV-2 viruses. In our physical chemistry lab in spring 2024, students practice kinetic models, SIR (Susceptible, Infected, and Recovered) and SIRV (Susceptible, Infected, Recovered, Vaccinated) using COVID-19 positive cases and vaccination data from World Health Organization (WHO). In this report, we further introduce virus breakthrough to the existing model updating it the SIRVB (Susceptible, Infectious, Recovered, Vaccinated, Breakthrough) model. We believe this is the simplest model possible to explain the COVID-19 kinetics in all countries in the past four years. Parameters obtained from such practice correlate with many indices of different countries. These models and parameters have significant value to researchers and policymakers in predicting the stages of future outbreaks of infectious diseases.

Towards the definition of a standard in TMS-EEG data preprocessing.

Combining Non-Invasive Brain Stimulation (NIBS) techniques with the recording of brain electrophysiological activity is an increasingly widespread approach in neuroscience. Particularly successful has been the simultaneous combination of Transcranial Magnetic Stimulation (TMS) and Electroencephalography (EEG). Unfortunately, the strong magnetic pulse required to effectively interact with brain activity inevitably induces artifacts in the concurrent EEG acquisition. Therefore, a careful but aggressive pre-processing is required to efficiently remove artifacts. Unfortunately, as already reported in the literature, different preprocessing approaches can introduce variability in the results. Here we aim at characterizing the three main TMS-EEG preprocessing pipelines currently available, namely ARTIST (Wu et al., 2018), TESA (Rogasch et al., 2017) and SOUND/SSP-SIR (Mutanen et al., 2018, 2016), providing an insight to researchers who need to choose between different approaches. Differently from previous works, we tested the pipelines using a synthetic TMS-EEG signal with a known ground-truth (the artifacts-free to-be-reconstructed signal). In this way, it was possible to assess the reliability of each pipeline precisely and quantitatively, providing a more robust reference for future research. In summary, we found that all pipelines performed well, but with differences in terms of the spatio-temporal precision of the ground-truth reconstruction. Crucially, the three pipelines impacted differently on the inter-trial variability, with ARTIST introducing inter-trial variability not already intrinsic to the ground-truth signal.

Quantifying indirect and direct vaccination effects arising in the SIR model.

Vaccination campaigns have both direct and indirect effects that act to control an infectious disease as it spreads through a population. Indirect effects arise when vaccinated individuals block disease transmission in any infection chain they are part of, and this in turn can benefit both vaccinated and unvaccinated individuals. Indirect effects are difficult to quantify in practice but, in this article, working with the susceptible-infected-recovered (SIR) model, they are analytically calculated in important cases, through pivoting on the final size formula for epidemics. Their relationship to herd immunity is also clarified. The analysis allows us to identify the important distinction between quantifying the indirect effects of vaccination at the 'population level' versus the 'per capita' level, which often results in radically different conclusions. As an example, our analysis unpacks why the population-level indirect effect can appear significantly larger than its per capita analogue. In addition, we consider a recently proposed epidemiological non-pharmaceutical intervention (by the means of recovered individuals) used over the COVID-19 pandemic, referred to as 'shielding', and study its impact on our mathematical analysis. The shielding scheme is extended to take advantage of vaccination including imperfect vaccination.

Calibration and Comparison of SIR, SEIR/SLIR, and SLAIR Models for Influenza Dynamics: Insights from the 2016-2017 Season in the Valencian Community, Spain.

Influenza and influenza-like illnesses (ILI) pose significant challenges to healthcare systems globally. Mathematical models play a crucial role in understanding their dynamics, calibrating them to specific scenarios, and making projections about their evolution over time. This study proposes a calibration process for three different but well-known compartmental models - SIR, SEIR/SLIR, and SLAIR - using influenza data from the 2016-2017 season in the Valencian Community, Spain. The calibration process involves indirect calibration for the SIR and SLIR models, requiring post-processing to compare model output with data, while the SLAIR model is directly calibrated through direct comparison. Our calibration results demonstrate remarkable consistency between the SIR and SLIR models, with slight variations observed in the SLAIR model due to its unique design and calibration strategy. Importantly, all models align with existing evidence and intuitions found in the medical literature. Our findings suggest that at the onset of the epidemiological season, a significant proportion of the population (ranging from 29.08% to 43.75% of the total population) may have already entered the recovered state, likely due to immunization from the previous season. Additionally, we estimate that the percentage of infected individuals seeking healthcare services ranges from 5.7% to 12.2%. Through a well-founded and calibrated modeling approach, our study contributes to supporting, settling, and quantifying current medical issues despite the inherent uncertainties involved in influenza dynamics. The full Mathematica code can be downloaded from https://munqu.webs.upv.es/software.html.

The study on the role of O-GlcNAcylation of SIRT3 in regulating mitochondrial oxidative stress during simulate myocardial ischemia-reperfusion.

Myocardial ischemia-reperfusion injury (MIRI) is a significant complication following reperfusion therapy after myocardial infarction. Mitochondrial oxidative stress is a critical factor in MIRI, and Sirtuin 3 (SIRT3), as a major mitochondrial deacetylase, plays a key protective role, with its activity potentially regulated by O-GlcNAcylation. This study used the H9C2 cell line to establish a simulated ischemia/reperfusion (SI/R) model, we utilized co-immunoprecipitated to validate the relationship between O-GlcNAc transferase (OGT) and SIRT3, demonstrated SIRT3 O-GlcNAcylation sites through LC-MS/MS, and performed site mutations using CRISPR/Cas9 technology. The results were validated using immunoblotting. SIRT3 and superoxide dismutase 2 (SOD2) activities were detected using a fluorometric assay, while mitochondrial reactive oxygen species (MROS) levels and cellular apoptosis were assessed using immunofluorescence. We have identified an interaction between SIRT3 and OGT, where SIRT3 undergoes dynamic O-GlcNAcylation at the S190 site, facilitating SIRT3 deacetylase activity. During SI/R, elevated levels of O-GlcNAcylation activate SOD2 by promoting SIRT3 enzyme activity, thereby inhibiting excessive MROS production. This significantly mitigates the occurrence of malignant autophagy in myocardial cells during reperfusion, promoting their survival. Conversely, blocking SIRT3 O-GlcNAcylation at the S190 site exacerbates SI/R injury. We demonstrate that O-GlcNAcylation is a crucial post-translational modification (PTM) of SIRT3 during SI/R, shedding light on a promising mechanism for future therapeutic approaches.

Vaccination strategies for different contact patterns: weighing epidemiological against economic outcomes.

The aim of this paper is to shed light on the economic and epidemiological trade-offs that emerge when choosing between different vaccination strategies. For that purpose we employ a setting with three age groups that differ with respect to their fatality rates. The model also accounts for heterogeneity in the transmission rates between and within these age groups. We compare the results for two different contact patterns, in terms of the total number of deceased, the total number of infected, the peak infection rate and the economic gains from different vaccination strategies. We find that fatalities are minimized by first vaccinating the elderly, except when vaccination is slow and the general transmission rate is relatively low. In this case deaths are minimized by first vaccinating the group that is mainly responsible for spreading of the virus. With regard to the other outcome variables it is best to vaccinate the group that drives the pandemic first. A trade-off may therefore emerge between reducing fatalities on the one hand and lowering the number of infected as well as maximizing the economic gains from vaccinations on the other hand.

Anti-infective properties of mung bean (Vigna radiata (L.)R. Wilczek) coat extract on Pseudomonas aeruginosa-infected Caenorhabditis elegans: Transcriptomics and pathway analysis.

ETHNOPHARMACOLOGICAL RELEVANCE: Mung bean coat has long been known for its wide-ranging health benefits, including antibacterial, anti-inflammatory, and immune-modulatory properties. For many years in China, mung beans have been employed in the therapeutic management of inflammation induced by pathogenic bacteria infection, yet the precise underlying protective mechanisms remain to be comprehensively elucidated. AIM OF THE STUDY: Given the growing concern over antibiotic resistance, there is a necessity to explore new anti-infective agents. Here, the anti-infective properties of Mung bean coat extract (MBCE) were investigated using a model of Pseudomonas aeruginosa-infected nematodes. MATERIALS AND METHODS: The protective effects of MBCE on Pseudomonas aeruginosa (PA14) infected nematodes were assessed by lifespan assay, reactive oxygen species (ROS) levels, transcriptomics, and Quantitative real-time PCR (qRT-PCR). RESULTS: MBCE significantly improved the survival rates and reduced ROS levels in infected worms. Transcriptomic profiling disclosed predominant KEGG pathway enrichments in immune responses, energy metabolism processes such as oxidative phosphorylation and the tricarboxylic acid cycle, alongside aging-related neurodegenerative diseases and longevity regulatory pathways like PI3K-AKT, MAPK, mTOR, and FOXO. qRT-PCR validation showed that MBCE upregulated antimicrobial peptides (spp-3, lys-1, lys-7, abf-2, cnc-2, nlp-33, clec-85), gram-negative responses (irg-3, src-2, grd-3, col-179), and mitochondrial function (mev-1) gene expressions, while downregulated insulin signaling-related (age-1, akt-1, akt-2, daf-15) gene expressions. Mutant strains lifespan analysis indicated that the nsy-1, sek-1, pmk-1, daf-2, aak-2, sir-2.1, and skn-1 were necessary for lifespan extension mediated by MBCE under PA14 infection, but not clk-1, isp-1, mev-1, or daf-16. CONCLUSION: Collectively, our findings suggested that MBCE increased the survival rates of PA14-infected worms by activating downstream antimicrobial and antioxidant gene expressions through modulation of MAPK, daf-2, aak-2, sir-2.1, and skn-1 pathways. The research underscored the potential of natural plant compounds to strengthen the body's defenses against infections, potentially mitigating harmful ROS levels and improving survival. Additionally, these findings elucidated the mechanisms by which these plant-derived compounds enhance the immune system, implying their potential utility as dietary supplements or as an alternative to conventional antibiotics.

Optimal time-dependent SUC model for COVID-19 pandemic in India.

In this paper, we propose a numerical algorithm to obtain the optimal epidemic parameters for a time-dependent Susceptible-Unidentified infected-Confirmed (tSUC) model. The tSUC model was developed to investigate the epidemiology of unconfirmed infection cases over an extended period. Among the epidemic parameters, the transmission rate can fluctuate significantly or remain stable due to various factors. For instance, if early intervention in an epidemic fails, the transmission rate may increase, whereas appropriate policies, including strict public health measures, can reduce the transmission rate. Therefore, we adaptively estimate the transmission rate to the given data using the linear change points of the number of new confirmed cases by the given cumulative confirmed data set, and the time-dependent transmission rate is interpolated based on the estimated transmission rates at linear change points. The proposed numerical algorithm preprocesses actual cumulative confirmed cases in India to smooth it and uses the preprocessed data to identify linear change points. Using these linear change points and the tSUC model, it finds the optimal time-dependent parameters that minimize the difference between the actual cumulative confirmed cases and the computed numerical solution in the least-squares sense. Numerical experiments demonstrate the numerical solution of the tSUC model using the optimal time-dependent parameters found by the proposed algorithm, validating the performance of the algorithm. Consequently, the proposed numerical algorithm calculates the time-dependent transmission rate for the actual cumulative confirmed cases in India, which can serve as a basis for analyzing the COVID-19 pandemic in India.

Positivity and Boundedness Preserving Numerical Scheme for a Stochastic Multigroup Susceptible-Infected-Recovering Epidemic Model with Age Structure.

Since the stochastic age-structured multigroup susceptible-infected-recovering (SIR) epidemic model is nonlinear, the solution of this model is hard to be explicitly represented. It is necessary to construct effective numerical methods so as to predict the number of infections. In addition, the stochastic age-structured multigroup SIR model has features of positivity and boundedness of the solution. Therefore, in this article, in order to ensure that the numerical and analytical solutions must have the same properties, by modifying the classical Euler-Maruyama (EM) scheme, we generate a positivity and boundedness preserving EM (PBPEM) method on temporal space for stochastic age-structured multigroup SIR model, which is proved to have a strong convergence to the true solution over finite time intervals. Moreover, by combining the standard finite element method and the PBPEM method, we propose a full-discrete scheme to show the numerical solutions, as well as analyze the error estimations. Finally, the full-discrete scheme is applied to a general stochastic two-group SIR model and the Chlamydia epidemic model, which shows the superiority of the numerical method.

How to correctly fit an SIR model to data from an SEIR model?

In epidemiology, realistic disease dynamics often require Susceptible-Exposed-Infected-Recovered (SEIR)-like models because they account for incubation periods before individuals become infectious. However, for the sake of analytical tractability, simpler Susceptible-Infected-Recovered (SIR) models are commonly used, despite their lack of biological realism. Bridging these models is crucial for accurately estimating parameters and fitting models to observed data, particularly in population-level studies of infectious diseases. This paper investigates stochastic versions of the SEIR and SIR frameworks and demonstrates that the SEIR model can be effectively approximated by a SIR model with time-dependent infection and recovery rates. The validity of this approximation is supported by the derivation of a large-population Functional Law of Large Numbers (FLLN) limit and a finite-population concentration inequality. To apply this approximation in practice, the paper introduces a parameter inference methodology based on the Dynamic Survival Analysis (DSA) survival analysis framework. This method enables the fitting of the SIR model to data simulated from the more complex SEIR dynamics, as illustrated through simulated experiments.

An Evaluation Model for Node Influence Based on Heuristic Spatiotemporal Features.

The accurate assessment of node influence is of vital significance for enhancing system stability. Given the structural redundancy problem triggered by the network topology deviation when an empirical network is copied, as well as the dynamic characteristics of the empirical network itself, it is difficult for traditional static assessment methods to effectively capture the dynamic evolution of node influence. Therefore, we propose a heuristic-based spatiotemporal feature node influence assessment model (HEIST). First, the zero-model method is applied to optimize the network-copying process and reduce the noise interference caused by network structure redundancy. Second, the copied network is divided into subnets, and feature modeling is performed to enhance the node influence differentiation. Third, node influence is quantified based on the spatiotemporal depth-perception module, which has a built-in local and global two-layer structure. At the local level, a graph convolutional neural network (GCN) is used to improve the spatial perception of node influence; it fuses the feature changes of the nodes in the subnetwork variation, combining this method with a long- and short-term memory network (LSTM) to enhance its ability to capture the depth evolution of node influence and improve the robustness of the assessment. Finally, a heuristic assessment algorithm is used to jointly optimize the influence strength of the nodes at different stages and quantify the node influence via a nonlinear optimization function. The experiments show that the Kendall coefficients exceed 90% in multiple datasets, proving that the model has good generalization performance in empirical networks.

Behind the Smile: Managing Class I Malocclusion and Protrusive Upper Incisors With Kalra Simultaneous Intrusion and Retraction (K-SIR) Mechanics.

Malocclusion is defined as any deviation from the ideal occlusal positions and the position of the specific teeth. Those that are common are numerous and affect a patient's stomatology and dental structures in appearance and utility. Class I is the most common type and favors the anterior relationship of both jaws, which lies between the second and third quartiles. Its cause is still unknown at the moment. It is even more frequent than usual occlusion. Class I malocclusion with an overjet of upper incisors less than 4 mm accompanied by type 2 of Dewey's modification also displays protruded upper incisors and a deep overbite. This case report's focus is to provide an extensive evaluation of the diagnostic process, management plan, and outcome for a patient who had presented with this specific dental abnormality and simultaneous intrusion and retraction mechanics for an anterior segment with Kalra Simultaneous Intrusion and Retraction (K-SIR) loops.

Possible counter-intuitive impact of local vaccine mandates for vaccine-preventable infectious diseases.

We modeled the impact of local vaccine mandates on the spread of vaccine-preventable infectious diseases, which in the absence of vaccines will mainly affect children. Examples of such diseases are measles, rubella, mumps, and pertussis. To model the spread of the pathogen, we used a stochastic SIR (susceptible, infectious, recovered) model with two levels of mixing in a closed population, often referred to as the household model. In this model, individuals make local contacts within a specific small subgroup of the population (e.g., within a household or a school class), while they also make global contacts with random people in the population at a much lower rate than the rate of local contacts. We considered what would happen if schools were given freedom to impose vaccine mandates on all of their pupils, except for the pupils that were exempt from vaccination because of medical reasons. We investigated first how such a mandate affected the probability of an outbreak of a disease. Furthermore, we focused on the probability that a pupil that was medically exempt from vaccination, would get infected during an outbreak. We showed that if the population vaccine coverage was close to the herd-immunity level, then both probabilities may increase if local vaccine mandates were implemented. This was caused by unvaccinated pupils possibly being moved to schools without mandates.

Carbon footprint analysis of wastewater treatment processes coupled with sludge in situ reduction.

The goal of this study was to assess the impacts or benefits of sludge in situ reduction (SIR) within wastewater treatment processes with relation to global warming potential in wastewater treatment plants, with a comprehensive consideration of wastewater and sludge treatment. The anaerobic side-stream reactor (ASSR) and the sludge process reduction activated sludge (SPRAS), two typical SIR technologies, were used to compare the carbon footprint analysis results with the conventional anaerobic - anoxic - oxic (AAO) process. Compared to the AAO, the ASSR with a typical sludge reduction efficiency (SRE) of 30 % increased greenhouse gas (GHG) emissions by 1.1 - 1.7 %, while the SPRAS with a SRE of 74 % reduced GHG emissions by 12.3 - 17.6 %. Electricity consumption (0.025 - 0.027 kg CO2-eq/m3), CO2 emissions (0.016 - 0.059 kg CO2-eq/m3), and N2O emissions (0.009 - 0.023 kg CO2-eq/m3) for the removal of secondary substrates released from sludge decay in the SIR processes were the major contributor to the increased GHG emissions from the wastewater treatment system. By lowering sludge production and the organic matter content in the sludge, the SIR processes significantly decreased the carbon footprints associated with sludge treatment and disposal. The threshold SREs of the ASSR for GHG reduction were 27.7 % and 34.6 % for the advanced dewatering - sanitary landfill and conventional dewatering - drying-incinerating routes, respectively. Overall, the SPRAS process could be considered as a cost-effective and sustainable low-carbon SIR technology for wastewater treatment.