Derivative‐based quadrature rules can improve the accuracy of numerical integration while reducing the computational effort required to achieve a prescribed accuracy. In this paper, four new three‐point derivative‐based semiopen Newton–Cotes (MSO–NC) quadrature rules are developed by incorporating first‐order derivative information at selected nodes within the integration interval. The proposed rules extend the classical three‐point semiopen Newton–Cotes formulas and increase their algebraic degree of precision while using only first‐order derivatives. Theoretical properties of the proposed methods, including the degree of precision, local and global error terms, and orders of accuracy, are established. Composite versions of the rules are also derived for practical computation. The proposed methods are tested on a range of regular, oscillatory, singular, and nearly singular integrals. Their performance is evaluated in terms of accuracy, computational cost, CPU time, and convergence behavior. Comparisons with existing derivative‐free and derivative‐based quadrature rules demonstrate that the proposed MSO–NC methods achieve higher accuracy with substantially lower computational cost. The results also show that the use of only first‐order derivatives provides an efficient alternative to existing approaches that require higher‐order derivative information.
Dengue disease burden is escalating globally, driven by climate‐induced shifts in temperature and precipitation that create increasingly suitable environments for vector mosquitoes. This study develops a fractional order dengue transmission model incorporating temperature‐dependent parameters to capture climatic effects on mosquito behavior and disease spread. The model incorporates Caputo fractional derivatives to capture memory‐dependent biological processes and introduces temperature‐dependent parameters that reflect the effects of temperature variation on the mosquito biting rate, transmission probabilities, and mortality rates. The model ensures nonnegativity and boundedness of all state variables, and the basic reproduction number R 0 is derived using the next‐generation approach. Analytical results show that the disease‐free equilibrium is locally asymptotically stable when R 0 < 1, while temperature variations significantly influence transmission intensity. The findings highlight the importance of fractional derivatives and temperature in understanding dengue outbreaks.
This study develops a novel mathematical model to examine the coinfection dynamics of COVID-19 and lung cancer. We develop a seven-compartment deterministic model that combines the acute viral transmission with the long-term oncogenic progression via modified susceptibility parameters, enabling to model the clinically observed synergistic exacerbation between the two diseases. We obtain disease-specific epidemic thresholds and demonstrate that the overall reproduction number is determined by the maximum of these individual thresholds. Stability analysis shows that the disease-free state is globally stable if the threshold is less than unity, and a unique endemic state appears if it is greater than unity. The sensitivity analysis consists of combining the analytical indices for lung cancer and the global statistical method for COVID-19 parameters. The analysis results show that the dominant factors affecting the epidemic outcomes are the rates of disease transmission and recovery. Numerical simulations show that coinfection results in an advance of epidemic peaks by 15–30 days, and in an increase of the equilibrium prevalence up to 47% when compared to single-disease scenarios. Integrated interventions are 40%–65% more effective than isolated strategies in reducing the coinfection burden. The work provides a rigorous mathematical framework for modeling multiple diseases with implications for public health policy and clinical management of high-risk populations.
This paper presents the double Laplace transform (DLT) technique for the exact solution treatment of the fractional-order Helmholtz equation. The DLT is proficient for addressing fractional-order partial derivatives and transforming the problem into an algebraic equation, which is the uniqueness of the present paper. Four numerical applications are examined to determine the effectiveness and validity of this technique.
