An innovative fractional-order evolutionary game theoretical study of personal protection, quarantine, and isolation policies for combating epidemic diseases.

This study uses imposed control techniques and vaccination game theory to study disease dynamics with transitory or diminishing immunity. Our model uses the ABC fractional-order derivative mechanism to show the effect of non-pharmaceutical interventions such as personal protection or awareness, quarantine, and isolation to simulate the essential control strategies against an infectious disease spread in an infinite and uniformly distributed population. A comprehensive evolutionary game theory study quantified the significant influence of people's vaccination choices, with government forces participating in vaccination programs to improve obligatory control measures to reduce epidemic spread. This model uses the intervention options described above as a control strategy to reduce disease prevalence in human societies. Again, our simulated results show that a combined control strategy works exquisitely when the disease spreads even faster. A sluggish dissemination rate slows an epidemic outbreak, but modest control techniques can reestablish a disease-free equilibrium. Preventive vaccination regulates the border between the three phases, while personal protection, quarantine, and isolation methods reduce disease transmission in existing places. Thus, successfully combining these three intervention measures reduces epidemic or pandemic size, as represented by line graphs and 3D surface diagrams. For the first time, we use a fractional-order derivate to display the phase-portrayed trajectory graph to show the model's dynamics if immunity wanes at a specific pace, considering various vaccination cost and effectiveness settings.

Analysis and simulation study of the HIV/AIDS model using the real cases.

We construct a model to investigate HIV/AIDS dynamics in real cases and study its mathematical analysis. The study examines the qualitative outcomes and confirms the local and global asymptotic stability of both the endemic equilibrium and the disease-free equilibrium. The model's criteria for exhibiting both local and global asymptotically stable behavior are examined. We compute the endemic equilibria and obtain the existence of a unique positive endemic equilibrium. The data is fitted to the model using the idea of nonlinear least-squares fitting. Accurate parameter values are achieved by fitting the data to the model using a 95% confidence interval. The basic reproduction number is computed using parameters that have been fitted or estimated. Sensitivity analysis is performed to discover the influential parameters that impact the reproduction number and the eradication of the disease. The results show that implementing preventive measures can reduce HIV/AIDS cases.

An effective and economic estimation of population mean in stratified random sampling using a linear cost function.

Improvement in the estimation of population mean has been an area of interest in sampling theory. So many estimators have been suggested for elevated estimation of the population mean in stratified random sampling, but there is still a gap for more closely estimating the population mean. In this paper, the authors propose a ratio-product-cum-exponential-cum-logarithmic type estimator for the enhanced estimation of population mean by implying one auxiliary variable in stratified random sampling using conventional ratio, exponential ratio, and logarithmic ratio type estimators. The suggested estimator is a generalization of ratio, exponential ratio, and logarithmic ratio type estimators, and therefore these are special cases of the proposed estimator. The proposed estimator's bias and MSE are determined and compared with those of influential estimators, with the linear cost function being used to investigate and compare alternatives. Use Cramer's rule to determine the optimal value of the proposed estimator. The proposed estimator is more effective than other existing estimators, according to theoretical observations. For various applications, we suggest using a proposed estimator with the minimal MSE, which is verified by a numerical example, to have practical applicability of theoretical conclusions in real life.