Research Article
Evaluation of Some Approximations of the Temperature Integral Used in Kinetic Analysis of Solid-state Reactions
Kim Hyon Chol*
,
Ri Kwang Il
Issue:
Volume 14, Issue 3, June 2026
Pages:
71-78
Received:
25 December 2025
Accepted:
15 January 2026
Published:
12 June 2026
Abstract: In general, thermal analysis is a very convenient way to study the kinetics of thermally activated solid reactions, and experiments involving thermally activated solid reactions typically occur under nonisothermal conditions. The experimental data analysis obtained under non-isothermal conditions includes a temperature integral, also called the Arrhenius integral, which is one of the integrals that belong to many interesting integrals that are important in engineering and have no analytical solution. There are many different approximations that can be applied to the processing of thermogravimetric analysis data, since there is no standard way to calculate the temperature integral. Many approximations of the temperature integral that are important to use determine the kinetic parameters, especially the activation energy, which are typically divided into two categories: exponential and rational approximations. In order to evaluate the accuracy of various approximations of the temperature integral, we consider several certain continuous intervals. When choosing an approximation of the temperature integral needed to analyze the experimental data, it is necessary to analyze the accuracy at different temperature intervals of the approximation and use the appropriate one. We present new rational, irrational and continued fractional approximations together with approximations of the temperature integral presented in several literatures and calculate the relative errors of their activation energies.
Abstract: In general, thermal analysis is a very convenient way to study the kinetics of thermally activated solid reactions, and experiments involving thermally activated solid reactions typically occur under nonisothermal conditions. The experimental data analysis obtained under non-isothermal conditions includes a temperature integral, also called the Arr...
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Research Article
Bayesian Survival and Mixed-Effects Modeling of Immune Persistence Under COVID-19 Boosting
Mohammedelameen Qurashi*,
Amal Haj Hagsddig
Issue:
Volume 14, Issue 3, June 2026
Pages:
79-89
Received:
14 June 2026
Accepted:
1 July 2026
Published:
24 July 2026
DOI:
10.11648/j.sjams.20261403.12
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Abstract: Post-vaccination immune persistence varies significantly across booster regimens, particularly between homologous (e.g., mRNA/mRNA) and heterologous (e.g., VV/mRNA) strategies. This heterogeneity poses challenges for public health planning and long-term immunity forecasting. In this study, we developed a novel statistical framework integrating Bayesian survival analysis with linear mixed-effects regression to jointly model longitudinal IgG dynamics and time-to-waning of protective immunity in a cohort of 334 individuals—206 previously infected and 128 infection-naïve—from real-world data collected between December 2022 and September 2023. Plasma optical density (OD) values from ELISA assays served as a proxy for anti-SARS-CoV-2 IgG levels. Participants were categorized by booster type (homologous vs. heterologous), prior infection status, and number of doses (2-4). Our integrated model revealed that heterologous boosting was associated with significantly slower IgG decay (hazard ratio HR = 0.62, 95% credible interval [0.48-0.79]) compared to homologous regimens. Moreover, prior SARS-CoV-2 infection independently enhanced both humoral and cellular immune persistence, with infected individuals showing 1.8-fold higher median OD values at 6+ months post-boost. The joint modeling approach successfully captured inter-individual variability through random slopes and intercepts while accounting for censoring in immune waning via a Weibull-based survival component. This framework provides a flexible, predictive tool for evaluating future booster strategies—not only for SARS-CoV-2 but also for other pathogens requiring durable immunity. Our findings support the immunological advantage of heterologous prime-boost schedules, especially when combined with natural infection, and underscore the value of methodological integration in longitudinal immunology research.
Abstract: Post-vaccination immune persistence varies significantly across booster regimens, particularly between homologous (e.g., mRNA/mRNA) and heterologous (e.g., VV/mRNA) strategies. This heterogeneity poses challenges for public health planning and long-term immunity forecasting. In this study, we developed a novel statistical framework integrating Baye...
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