Time-dependent Transmission Research Articles

Dynamics of delay epidemic model with periodic transmission rate

We introduce novel epidemic models with single and two strains described by systems of delay differential equations with a periodic time-dependent disease transmission rate, and based on the number of newly infected individuals. Transitions between infected, recovered, and returning to susceptible compartments due to waning immunity are determined by the accompanying time delays. Positiveness, existence and uniqueness of solutions are demonstrated with the help of fixed point theory. Reducing delay differential equations to integral equations facilitates determining the analytical estimation of the equilibrium solutions. When there are two strains, they compete together, and the strain with a larger basic reproduction number dominates in the population. However, both strains coexist, and the magnitudes of epidemic outbreaks are governed by the basic reproduction numbers. The outlines of this work are verified through comparison with seasonal influenza data.

Non-linear dynamics and control of COVID-19 in india revisited : evidence of synergistic, antagonistic and threshold effects

Various researchers have investigated the COVID-19 pandemic dynamics since 2020 focusing on various aspects of the epidemics. However, the non-linear dynamics of this epidemic is still not well understood. India having the largest population in the world with wide cultural, genomics, and immunity diversity is being considered a suitable case for present investigation to generate the crucial information of non-linear phenomena during the first two waves of the epidemics. An SIRD model is suggested, integrating varying transmission, recovery, and mortality rates over time to explore the nonlinear behavior of the epidemic in India. The time-dependent transmission, recovery, and mortality are calculated using the finite difference method with the aid of actual data released by the Indian government, for the periods before and during the lockdown phases. The novel results generated from the model show evidence of synergistic, antagonistic, and threshold effects and the role of various measures in controlling these epidemic trends.

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.

Modelling the Time-varying Transmission of Wild Poliovirus in Pakistan

Aims/Objectives: The efforts to eradicate the wild poliovirus since 1988 have successfully reduced its global prevalence by 99%. However, as of 2024, Pakistan and Afghanistan remain the only two endemic countries facing the virus transmission. This study employs a transmission dynamic model to understand the persistence of wild poliovirus type 1 (WPV1) in Pakistan. Study Design: An ordinary differential equations-based deterministic type of mathematical model was developed. Place and Duration of Study: Department of Epidemiology and Public Health and Institute of Microbiology, University of Agriculture Faisalabad, March 2023 to August 2023. Methodology: We included the number of reported polio cases and the proportion of missed children by supplementary immunization activities (SIAs) across the country from 2017-2022. The model considered both human-human and environment-human virus transmission through sewage contamination and these are represented by time-dependent transmission rate parameters. The parameter estimation was done by model fitting to the reported data of WPV1 cases. The model simulations then predicted the future polio infections in Pakistan. Results: Our analysis identified that the asymptomatic infectious population missed by the SIAs is the major contributor to disease persistence in the country. Moreover, the environment can contribute to virus transmission in areas with poor WASH infrastructure and under-immunized populations. The estimated basic reproduction number through the next-generation matrix method was 1.61 while the estimated effective reproduction number was 0.12. The model showed a better predictive ability than constant transmission rate models. The numerical simulations considering the reduction in the virus-shedding rate by the asymptomatic population resulted in an 85% reduction in future polio cases in Pakistan. Conclusion: The results suggest that endemic virus transmission will continue subject to the current higher vaccination coverage across the country. The model can be further utilized to guide eradication efforts for targeted allocation of preemptive measures.

Dual-strain dynamics of COVID-19 variants in India: Modeling, analysis, and implications for pandemic control

This study introduces a detailed compartmental model developed to understand the complex dynamics of COVID-19 transmission, focusing on the Delta and Omicron variants in India. The model tracks disease progression through different population compartments, considering factors like vaccination, time-dependent transmission, economic burden and COVID-19 death rates, loss of vaccine-induced immunity, and the transition of asymptomatic cases to recovery. The model is validated against established epidemiological knowledge and real-world data, emphasizing dynamic parameterization and accurate representation of immunity dynamics. The basic reproduction number for both variants is calculated, and sensitivity analysis for various parameters is conducted. Time-dependent parameters are estimated using the discrete inverse method. The study also explores the economic burden, impact of different types of masks, vaccine efficacy, and vaccine-induced immunity through numerical analysis.

A re-activation model for 169Yb intensity modulated brachytherapy sources accounting for spatiotemporal isotopic composition.

Intensity modulated brachytherapy based on partially shielded intracavitary and interstitial applicators is possible with a cost-effective 169Yb production method. 169Yb is a traditionally expensive isotope suitable for this purpose, with an average γ-ray energy of 93keV. Re-activating a single 169Yb source multiple times in a nuclear reactor between clinical uses was shown to theoretically reduce cost by approximately 75% relative to conventional single-activation sources. With re-activation, substantial spatiotemporal variation in isotopic source composition is expected between activations via 168Yb burnup and 169Yb decay, resulting in time dependent neutron transmission, precursor usage, and reactor time needed per re-activation. To introduce a generalized model of radioactive source production that accounts for spatiotemporal variation in isotopic source composition to improve the efficiency estimate of the 169Yb production process, with and without re-activation. A time-dependent thermal neutron transport, isotope transmutation, and decay model was developed. Thermal neutron flux within partitioned sub-volumes of a cylindrical active source was calculated by raytracing through the spatiotemporal dependent isotopic composition throughout the source, accounting for thermal neutron attenuation along each ray. The model was benchmarked, generalized, and applied to a variety of active source dimensions with radii ranging from 0.4 to 1.0mm, lengths from 2.5 to 10.5mm, and volumes from 0.31 to 7.85 mm3, at thermal neutron fluxes from 1×1014to1×1015 n cm-2 s-1. The 168Yb-Yb2O3 density was 8.5g cm-3 with 82% 168Yb-enrichment. As an example, a reference re-activatable 169Yb active source (RRS) constructed of 82%-enriched 168Yb-Yb2O3 precursor was modeled, with 0.6mm diameter, 10.5mm length, 3 mm3 volume, 8.5g cm-3 density, and a thermal neutron activation flux of 4 × 1014 neutronscm-2s-1. The average clinical 169Yb activity for a 0.99 versus 0.31 mm3 source dropped from 20.1 to 7.5Ci for a 4×1014ncm-2s-1 activation flux and from 20.9 to 8.7Ci for a 1×1015ncm-2s-1 activation flux. For thermal neutron fluxes ≥2×1014ncm-2s-1, total precursor and reactor time per clinic-year were maximized at a source volume of 0.99 mm3 and reached a near minimum at 3mm3. When the spatiotemporal isotopic composition effect was accounted for, average thermal neutron transmission increased over RRS lifetime from 23.6% to 55.9%. A 28% reduction (42.5 days to 30.6 days) in the reactor time needed per clinic-year for the RRS is predicted relative to a model that does not account for spatiotemporal isotopic composition effects. Accounting for spatiotemporal isotopic composition effects within the RRS results in a 28% reduction in the reactor time per clinic-year relative to the case in which such changes are not accounted for. Smaller volume sources had a disadvantage in that average clinical 169Yb activity decreased substantially below 20Ci for source volumes under 1mm3. Increasing source volume above 3 mm3 adds little value in precursor and reactor time savings and has a geometric disadvantage.

Dynamic behavior of mixed convection heat transfer among horizontal co-axial fixed pipes at varying temperatures: Efficiency of cylindrical heat sink

The aim of the current research is to highlight the time-dependent properties of laminar convective thermal transmission inside a semi-infinite pipe, with an emphasis on flow frequencies that impact inter-fluid momentum and energy. The implicit finite difference approach is used to solve two-dimensional mathematical model composed of nonlinear partial differential equations. The research includes forecasting thermal performance of time-dependent flow in a pipe over several parameter ranges relevant to the flow model. The obtained forecasts were emphasized graphically. The numerical solutions were separated into steady and unsteady components, with the steady component yielding findings that were then used to determine the time dependent surface shearness and energy shearness in the time dependent phase. The stable component of the investigation revealed that raising the buoyancy force parameter and the impact of viscous dissipation significantly improved the flow velocity pattern and heat distributions throughout the flow domain. While the amplitude of time dependent surface shearness varied somewhat across various buoyancy force parameter values, the amplitude of time dependent heat transmission rates varied significantly. This study sheds light on the interaction of several characteristics, such as buoyancy force effects and internal energy loss, on time-dependent thermal energy flow inside a semi-infinite pipe subjected to laminar convective flow. It is worth noting that the amplitude of the time dependent rate of heat transmission shows more noticeable variations with different values of the buoyancy force parameter, in contrast to the minute change in the amplitude of the time dependent surface sheerness.

Assessment of vaccination and underreporting on COVID-19 infections in Turkey based on effective reproduction number

In this paper, we introduce a SEIR-type COVID-19 model where the infected class is further divided into subclasses with individuals in intensive care (ICUs) and ventilation units. The model is calibrated with the symptomatic COVID-19 cases, deaths, and the number of patients in ICUs and ventilation units as reported by Republic of Turkey, Ministry of Health for the period 11 March 2020 through 30 May 2020 when the nationwide lockdown is in order. COVID-19 interventions in Turkey are incorporated into the model to detect the future trend of the outbreak accurately. We tested the effect of underreporting and we found that the peaks of the disease differ significantly depending on the rate of underreporting, however, the timing of the peaks remains constant. The lockdown is lifted on 1 June, and the model is modified to include a time-dependent transmission rate which is linked to the effective reproduction number [Formula: see text] through basic reproduction number [Formula: see text]. The modified model captures the changing dynamics and peaks of the outbreak successfully. With the onset of vaccination on 13 January 2021, we augment the model with the vaccination class to investigate the impact of vaccination rate and efficacy. We observe that vaccination rate is a more critical parameter than the vaccine efficacy to eliminate the disease successfully.

An agent-based nested model integrating within-host and between-host mechanisms to predict an epidemic

The COVID-19 pandemic has remarkably heightened concerns regarding the prediction of communicable disease spread. This study introduces an innovative agent-based modeling approach. In this model, the quantification of human-to-human transmission aligns with the dynamic variations in the viral load within an individual, termed “within-host” and adheres to the susceptible–infected–recovered (SIR) process, referred to as “between-host.” Variations in the viral load over time affect the infectivity between individual agents. This model diverges from the traditional SIR model, which employs a constant transmission probability, by incorporating a dynamic, time-dependent transmission probability influenced by the viral load in a host agent. The proposed model retains the time-integrated transmission probability characteristic of the conventional SIR model. As observed in this model, the overall epidemic size remains consistent with the predictions of the standard SIR model. Nonetheless, compared to predictions based on the classical SIR process, notable differences existed in the peak number of the infected individuals and the timing of this peak. These nontrivial differences are induced by the direct correlation between the time-evolving transmission probability and the viral load within a host agent. The developed model can inform targeted intervention strategies and public health policies by providing detailed insights into disease spread dynamics, crucial for effectively managing epidemics.

Multistability and chaos in SEIRS epidemic model with a periodic time-dependent transmission rate

In this work, we study the dynamics of a susceptible-exposed-infectious-recovered-susceptible epidemic model with a periodic time-dependent transmission rate. Emphasizing the influence of the seasonality frequency on the system dynamics, we analyze the largest Lyapunov exponent along parameter planes finding large chaotic regions. Furthermore, in some ranges, there are shrimp-like periodic structures. We highlight the system multistability, identifying the coexistence of periodic orbits for the same parameter values, with the infections maximum distinguishing by up one order of magnitude, depending only on the initial conditions. In this case, the basins of attraction have self-similarity. Parametric configurations, for which both periodic and non-periodic orbits occur, cover 13.20% of the evaluated range. We also identified the coexistence of periodic and chaotic attractors with different maxima of infectious cases, where the periodic scenario peak reaches approximately 50% higher than the chaotic one.

Modeling the Dynamic Effects of Human Mobility and Airborne Particulate Matter on the Spread of COVID-19

Identifying the relationship between human mobility, air pollution, and communicable disease poses a challenge for impact evaluation and public health planning. Specifically, Coronavirus disease 2019 (COVID-19) and air pollution from fine particulates (PM2.5), by which human mobility is mediated in a public health emergency. To describe the interplay between human mobility and PM2.5 during the spread of COVID-19, we proposed a nonlinear model of the time-dependent transmission rate as a function of these factors. A compartmental epidemic model, together with daily confirmed case data in Bangkok, Thailand during 2020–2021, was used to estimate the intrinsic parameters that can determine the impact on the transmission dynamic of the two earlier outbreaks. The results suggested a positive association between mobility and transmission, but this was strongly dependent on the context and the temporal characteristics of the data. For the ascending phase of an epidemic, the estimated coefficient of mobility variable in the second wave was greater than in the first wave, but the value of the mobility component in the transmission rate was smaller. Due to the influence of the baseline value and PM2.5, the estimated basic reproduction number of the second wave was higher than that of the first wave, even though mobility had a greater influence. For the descending phase, the value of the mobility component in the second wave was greater, due to the negative value of the estimated mobility coefficient. Despite this scaling effect, the results suggest a negative association between PM2.5 and the transmission rates. Although this conclusion agrees with some previous studies, the true effect of PM2.5 remains inconclusive and requires further investigation.

DECIPHERING DYNAMICS OF COVID-19 OUTBREAK IN INDIA: AN AGE-STRUCTURED MODEL

The dynamics of infectious disease transmission depends on social contact patterns and the precautions people take to minimize disease transmission. The social contact pattern varies depending on the community at large age distribution at work, school, and recreation. Consequently, knowing the age-specific prevalence and incidence of infectious diseases is critical for predicting future disease burden and the efficacy of interventions like vaccination. In this study, we use an SEIR age-structured multi-group epidemic model to understand how social contact affects disease control. We construct location-specific social contact matrices to observe that how social mixing affects disease spread. For mathematical analysis, we compute the basic reproduction number [Formula: see text] and exhibit the global behavior of the system in terms of [Formula: see text]. We also estimate the transmission rate using the empirical data of COVID-19 for India from 1 September 2020, to 31 December 2020. We simulate the lifting of non-pharmaceutical interventions by allowing people to return to work in phases and investigate its impact. Our findings imply that raising awareness in symptomatic infected individuals aged 20–49 years can help in reducing the number of infected individuals. When some schools are partially open, awareness in symptomatic infected individuals in school-age groups also plays a significant role in reducing disease cases. The simulation results also suggest that limiting contact at school and other gathering places could significantly lower the number of instances. Using the least square approach, we show that the time-dependent transmission rate is more realistic than the constant spread rate for COVID-19 in India. To reduce the COVID-19 burden, we obtain that gradually loosening control measures could flatten and lower other peaks. Our findings may help health policymakers to decide on timely age-based vaccination distribution strategies and control measures.

Epidemic Waves in a Stochastic SIRVI Epidemic Model Incorporating the Ornstein–Uhlenbeck Process

The worldwide data for COVID-19 for active, infected individuals in multiple waves show that traditional epidemic models with constant parameters are not able to capture this kind of disease behavior. We solved this major open mathematical problem in this report. We first consider the disease transmission rate for the stochastic SIRVI epidemic model, which satisfies the mean-reverting Ornstein–Uhlenbeck (OU) process, and we propose a new stochastic SIRVI model. We then showed the existence and uniqueness of the global solution and obtained sufficient conditions for the persistent mean and exponential extinction of infectious disease, which have not been given before. In the second part, we derive a nonlinear system of differential equations for the time-dependent transmission rate from the deterministic SIRVI model and present an algorithm to compute the time-dependent transmission rate directly from the given active, infected individuals’ data. We then show that the time-dependent transmission obtained from and perturbed by the Ornstein–Uhlenbeck process could be represented after using a smoothing technique using a finite linear combination of a Gaussian radial basis function, which was obtained from our algorithm. This novel computer-assisted proof provides a theoretical basis for other epidemic models and epidemic waves. Finally, some numerical solutions of the stochastic SIRVI model are presented using COVID-19 data from Saudi Arabia and Austria.

Epidemic dynamics with time-varying transmission risk reveal the role of disease stage-dependent infectiousness

A key characteristic of acute communicable diseases is the infectiousness that varies over time as the infection dynamics evolve within a host, which influences the risk of transmission in different stages of the disease. Despite the evidence of time-varying transmission risk, most dynamic models of epidemics assume a constant transmission rate during the infectious period. Recent work has shown the difference in epidemic dynamics when this assumption is relaxed and different transmission rates are used by discretizing the infectious period into multiple sub-periods. Here, we develop an age-structured model to integrate a continuous time-varying transmission risk, based on an established correlation between the viral dynamics and infectiousness profile. Taking into account the natural history and parameter estimates of COVID-19 caused by the original strain of SARS-CoV-2, we demonstrate the difference in temporal epidemic dynamics when a continuous time-varying transmission probability is used as compared to multiple constant transmission probabilities. Our results show a significant difference between the incidence curves in terms of the magnitude and peak time, even when the reproduction number and total number of infections are the same for continuous and discrete transmission probabilities. Finally, we demonstrate the spurious outcome of preventing an epidemic through the isolation of infectious individuals when constant transmission probabilities are used, highlighting the importance of integrating a continuous time-dependent transmission parameter in dynamic models. These findings suggest a more cautious interpretation of model outcomes, especially those that are intended to evaluate the effectiveness of interventions and inform policy decisions for disease mitigation strategies.

Measurement of Time Dependent Reflection, Transmission, and Absorption in Laser Driven Silicon and GaAs Switches for 250 GHz Radiation.

The reflectance and transmittance of Si and GaAs wafers irradiated by a 6 ns pulsed, 532 nm laser have been studied for s- and p-polarized 250 GHz radiation as a function of laser fluence and time. The measurements were carried out using precision timing of the and signals, allowing an accurate determination of the absorptance where . Both wafers had a maximum reflectance above 90% for a laser fluence . Both also showed an absorptance peak of ~50% lasting ~2 ns during the risetime of the laser pulse. Experimental results were compared with a stratified medium theory using the Vogel model for the carrier lifetime and the Drude model for permittivity. Modeling showed that the large absorptance at the early part of the rise of the laser pulse was due to the creation of a lossy, low carrier density layer. For Si, the measured and were in very good agreement with theory on both the nanosecond time scale and the microsecond scale. For GaAs, the agreement was very good on the nanosecond scale but only qualitatively correct on the microsecond scale. These results may be useful for planning applications of laser driven semiconductor switches.

Extreme Air Sensitivity and Nonself-Limited Oxidation of Two-Dimensional Magnetic Tellurides

The two-dimensional (2D) self-intercalated van der Waals magnets, chromium tellurides (Cr1+δTe2), with room temperature ferromagnetism and exotic topological spin textures, have emerged as an attractive platform for the development of ultrathin spintronic devices. While many prior studies claim Cr1+δTe2 are air-stable, which is crucial for practical applications, we demonstrate that within only minutes of exposure to air dramatic changes occur in the Raman and X-ray photoelectron spectroscopy spectra of nanoplates at room temperature. Time-dependent magnetization measurements and transmission electron microscopy studies suggested the rapid oxidation is not self-limited and has distinct processes on the surfaces and edges. Density functional theory calculations confirmed the spontaneous oxygen adsorption on the surface and the thermodynamically favorable oxidation process. These findings demonstrate unambiguously that the surface of Cr1+δTe2 is extremely air-sensitive, highlighting the necessity of surface protection for fundamental studies of intrinsic 2D magnetism and practical applications of advanced spintronic devices.

A mathematical interpretation for outbreaks of bacterial meningitis under the effect of time-dependent transmission parameters.

We consider a SIR-type compartmental model divided into two age classes to explain the seasonal exacerbations of bacterial meningitis, especially among children outside of the meningitis belt. We describe the seasonal forcing through time-dependent transmission parameters that may represent the outbreak of the meningitis cases after the annual pilgrimage period (Hajj) or uncontrolled inflows of irregular immigrants. We present and analyse a mathematical model with time-dependent transmission. We consider not only periodic functions in the analysis but also general non-periodic transmission processes. We show that the long-time average values of transmission functions can be used as a stability marker of the equilibrium. Furthermore, we interpret the basic reproduction number in case of time-dependent transmission functions. Numerical simulations support and help visualize the theoretical results.

Modeling the time-dependent transmission rate using gaussian pulses for analyzing the COVID-19 outbreaks in the world

In this work, an SEIR epidemic model with time-dependent transmission rate parameters for the multiple waves of COVID-19 infection was investigated. It is assumed that the transmission rate is determined by the superposition of the Gaussian pulses. The interaction of these dynamics is represented by recursive equations. Analysis of the overall dynamics of disease spread is determined by the effective reproduction number Re(t) produced throughout the infection period. The study managed to show the evolution of the epidemic over time and provided important information about the occurrence of multiple waves of COVID-19 infection in the world and Indonesia.

Analysis of SIRVI model with time dependent coefficients and the effect of vaccination on the transmission rate and COVID-19 epidemic waves.

COVID-19 epidemic models with constant transmission rate cannot capture the patterns of the infection data in the presence of pharmaceutical and non-pharmaceutical interventions during a pandemic. Because of this, a new modification of SIR model that contain the vaccination compartment with time dependent coefficients and weak/loss-immunity is explored. Literature review confirms that the effect of vaccination on the time dependent transmission rate is still an open problem. This study answers this open problem. In this study, we first prove the well-posedness and investigate the model dynamics to show their continuous dependence on the model parameters. We then provide an algorithm to derive the time-dependent transmission function for the epidemiologic model and the data of the infected cases. The derived coupled nonlinear differential equations show the effect of vaccination on the transmission rate. Unlike previous studies, we first filter the published data and solve the nonlinear coupled differential equations using the finite difference technique, where the coefficient of the coupled nonlinear differential equations is a function of given data. We then show that time-dependent transmission function can be represented by linear combinations of Gaussian radial base function. We then validate the prediction of our models using numerical simulations, where we used the published data of COVID-19 confirmed cases by the Ministries of Health in Saudi Arabia and Poland. Finally, the numerical solutions of a SIRVI model with time dependent transmission rate show that the waves for currently active cases are in good agreement with the data of Saudi Arabia and Poland.

Uncertainty quantification in mechanistic epidemic models via cross-entropy approximate Bayesian computation.

This paper proposes a data-driven approximate Bayesian computation framework for parameter estimation and uncertainty quantification of epidemic models, which incorporates two novelties: (i) the identification of the initial conditions by using plausible dynamic states that are compatible with observational data; (ii) learning of an informative prior distribution for the model parameters via the cross-entropy method. The new methodology's effectiveness is illustrated with the aid of actual data from the COVID-19 epidemic in Rio de Janeiro city in Brazil, employing an ordinary differential equation-based model with a generalized SEIR mechanistic structure that includes time-dependent transmission rate, asymptomatics, and hospitalizations. A minimization problem with two cost terms (number of hospitalizations and deaths) is formulated, and twelve parameters are identified. The calibrated model provides a consistent description of the available data, able to extrapolate forecasts over a few weeks, making the proposed methodology very appealing for real-time epidemic modeling.