Assume a (semi)parametrically efficient estimator is given of the Euclidean parameter in a (semi)parametric model. A submodel is obtained by constraining this model in that a continuously differentiable function of the Euclidean parameter vanishes. We present an explicit method to construct (semi)parametrically efficient estimators of the Euclidean parameter in such equality constrained submodels and prove their efficiency. Our construction is based solely on the original efficient estimator and the constraining function.

The authors present a mathematical framework for modelling dependence between biometric comparison scores in likelihood‐based fusion by copula models. The pseudo‐maximum likelihood estimator for the copula parameters and its asymptotic performance are studied. For a given objective performance measure in a realistic scenario, a resampling method for choosing the best copula pair is proposed. Finally, the proposed method is tested on some public biometric databases from fingerprint, face, speaker, and video‐based gait recognitions under some common objective performance measures: maximising acceptance rate at fixed false acceptance rate, minimising half total error rate, and minimising discrimination loss.

A family of Sigmoidal non-linear models is commonly used to determine the critical period of weed control (CPWC) and acceptable yield loss (AYL) in annual crops. We tried to prove another non-linear model to determine CPWC and AYL in a soybean agroforestry system with kayu putih. The three-year experiment (from 2019–2021) was conducted using a randomised complete block design factorial with five blocks as replications. The treatments comprised weedy and weed-free periods. Non-linear models comprised 45 functions. The results show that the Sigmoidal and Dose-Response Curve (DRC) families were the most suitable for estimating CPWC and AYL. The best fitted non-linear model for weedy and weed-free periods in the dry season used the Sigmoidal family consisting of the Weibull and Richards models, while in the wet season the best fit was obtained using the DRC and Sigmoidal families consisting of the DR-Hill and Richards models, respectively. The CPWC of soybean in the dry season for AYL was 5, 10, and 15%, beginning at 20, 22, and 24 days after emergence (DAE) and ended at 56, 54, and 52 DAE. The AYL in the wet season started at 20, 23, and 26 DAE and ended at 59, 53, and 49 DAE.

This study presented a glioma growth model that accounts for drug-sensitive and drug-resistant cells in response to chemotherapy and anti-angiogenic therapy. Chemotherapy induces mutations in drug-sensitive cells, leading to the emergence of drug-resistant cells and highlighting the benefits of combined therapy. Anti-angiogenic therapy can mitigate mutations by inducing angiogenic dormancy. We have identified two reproduction numbers associated with the non-cell and disease-free states. Numerical sensitivity analysis has highlighted influential parameters that control glioma growth dynamics, emphasizing the interactions between drug-sensitive and drug-resistant cells. To reduce glioma endemicity among sensitive cases, it was recommended to decrease chemotherapy expenditure, increase angiogenic dormancy, and adjust chemotherapy infusion rates. In addition, to combat resistance to glioma endemicity, enhancing angiogenic dormancy is crucial.

We propose a simple parameter estimation method for the Susceptible-Infectious-Recovered (SIR) model. This method offers explicit estimates of parameters using second-order numerical derivatives to construct empirical parameters. In addition, the method constructs confidence intervals, providing a robust assessment of parameter uncertainty. To validate the accuracy of our method, we applied it to simulated data, in order to demonstrate its effectiveness in accurately estimating the true model parameters. Furthermore, we applied this method to actual COVID-19 case data from the USA, Indonesia, and the Philippines. This application enables the estimation of parameters and reproductive numbers, along with their confidence intervals, thus underscoring the efficacy of our technique. Notably, the parameter estimates obtained through our approach successfully predicted the case numbers in all three countries, confirming its predictive reliability. Our method offers significant advantages in terms of simplicity and accuracy, making it an invaluable tool for epidemiological modeling and public health planning.

This study presents a mathematical model of glioma growth dynamics with drug resistance, capturing interactions among five cell populations – glial cells, sensitive and resistant glioma cells, endothelial cells, and neurons – alongside chemotherapy and antiangiogenic therapy. Glioma, a malignant tumor originating in glial cells, undergoes chemotherapy-induced mutations, leading to drug-resistant variants that affect both tumor and normal cells. The model incorporates a Holling Type II response function to optimize treatment doses while inducing angiogenic dormancy. Stability analysis identifies three equilibrium points – two stable and one unstable – while numerical simulations using phase portraits and trajectory diagrams illustrate the impact of combined therapies. This model provides insights into glioma progression and drug resistance, emphasizing the efficacy of combined therapies for optimizing treatment strategies.