Partial Differential Equations in Applied Mathematics最新文献

{"title":"Dynamics of COVID-malaria co-infection with optimal control and cost-effectiveness analysis","authors":"Shikha Saha ,&nbsp;Amit Kumar Saha ,&nbsp;Chandra Nath Podder","doi":"10.1016/j.padiff.2025.101217","DOIUrl":"10.1016/j.padiff.2025.101217","url":null,"abstract":"<div><div>Due to the geographic overlap between the distributions of COVID-19 and malaria, co-infection between these diseases is highly possible and could result in severe health issues. To understand the disease dynamics of the co-infection, a new mathematical model, which incorporates vaccination as an intervention, is formulated. Theoretical analysis suggests that both the sub-models (COVID-19-only and malaria-only sub-models) and the full model undergo backward bifurcation when their respective reproduction number is less than unity. It further suggests that in the absence of re-infection both the sub-models and the full model have a globally asymptotically stable disease free equilibrium whenever the corresponding reproduction number is less than unity. The study further reveals that malaria infection may increase the risk of COVID-19, whereas COVID-19 infection may not always increase the risk of malaria. Numerical simulation also suggests that COVID-19 fatality rate increases by approximately 5 folds due to co-infection with malaria while co-infection with COVID-19 may not have significant effect on malaria fatality rate. It again shows that malaria cases can be reduced by approximately 60% if 90% individuals use non-pharmaceutical interventions (NPIs), such as nets and repellents of 90% efficacy. Using the expression of the vaccine-induced herd immunity threshold and contour plot it is shown that at least 75% individuals should be vaccinated with a vaccine of 85% efficacy to achieve herd immunity against malaria. The study also shows that strategy C (prevention strategy for both COVID-19 and malaria) is the most cost-effective strategy to mitigate the burden of co-infection.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101217"},"PeriodicalIF":0.0,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144071575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A hybrid analytical method for fractional order Klein–Gordon and Burgers equations","authors":"Huda Omran Altaie ,&nbsp;Adel Rashed A. Ali ,&nbsp;Ghaith Fadhil Abbas ,&nbsp;Ali Hasan Ali","doi":"10.1016/j.padiff.2025.101220","DOIUrl":"10.1016/j.padiff.2025.101220","url":null,"abstract":"<div><div>In this study, fractional-order partial differential equations (FPDEs), specifically the Klein–Gordon equation (KGE) and the Burgers equation, are analytically solved using a modified and combined version of the Elzaki Decomposition Technique (ETADM). To assess the efficacy and robustness of the proposed approach, several examples are provided to obtain analytical and numerical results related to the KGE and the Burgers equation. Furthermore, the proposed techniques yield convergent series solutions with well-defined components, without the need for perturbation or linearization. Additionally, we compare several methods for solving differential equations arising in physics and engineering, including ETADM, the Variational Iteration Method (VIM), and the Adomian Decomposition Method (ADM). For comparison and validation, three examples are presented, along with the results obtained using both ETADM and VIM.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101220"},"PeriodicalIF":0.0,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143948222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cross-diffusion effects of viscous heating hydromagnetic Casson fluid flow in permeable vertical media with radiation and heat loss","authors":"B. Prabhakar Reddy ,&nbsp;MD. Shamshuddin ,&nbsp;S.O. Salawu ,&nbsp;M. Paul Matao","doi":"10.1016/j.padiff.2025.101225","DOIUrl":"10.1016/j.padiff.2025.101225","url":null,"abstract":"<div><div>This investigation is on Casson fluid transport's cross-diffusion and thermal dissipation along an oscillatory semi-infinite vertical geometry and the angled magnetic field. The study's novelty lies in the simultaneous consideration of viscous heating, cross-diffusion, and hydromagnetic effects in a Casson fluid model with heat loss an aspect scarcely addressed in previous studies. This research provides a comprehensive framework for understanding complex thermal-fluid interactions in industrial applications such as polymer processing, geothermal energy systems, and porous media heat exchangers. The complex partial differential equations (PDEs) system is converted into highly non-linear PDEs via non-dimensionalization variables. The nonlinear differential equations are solved by the numerical technique finite difference method (FDM) with suitable conditions. The flow, thermal, and concentration fields are examined for the obtained physical terms via graphical illustration. The skin friction, temperature, and mass gradients are evaluated graphically at the plate surface. As noticed, the temperature and mass buoyancy forces raised the stream rate field, but the Casson parameters have shown the opposite influence. The skin friction is strengthened by the porosity parameter but decreased with magnetic field and thermal and mass buoyancy forces. The viscous dissipation, heat absorption, and Dufour effects raised the heat gradient. The mass gradient is boosted with the Soret number, and the chemical reaction exposed the opposite trend. Finally, the investigation outcomes are meticulously verified with formerly reported results in an asymptotic situation.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101225"},"PeriodicalIF":0.0,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144083690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the classification of group invariant solutions of the Barenblatt–Gilman model by a one-dimensional system of subalgebras","authors":"Akhtar Hussain,&nbsp;M. Usman","doi":"10.1016/j.padiff.2025.101176","DOIUrl":"10.1016/j.padiff.2025.101176","url":null,"abstract":"<div><div>The Barenblatt–Gilman (BG) equation, which simulates nonequilibrium countercurrent capillary impregnation, is discussed in this study. By applying symmetry classification to the nonlinear function <span><math><mrow><mi>Φ</mi><mrow><mo>(</mo><mi>σ</mi><mo>)</mo></mrow></mrow></math></span>, six distinct cases emerge. In the general case, <span><math><mrow><mi>Φ</mi><mrow><mo>(</mo><mi>σ</mi><mo>)</mo></mrow></mrow></math></span> yields a three-dimensional principal algebra. The other cases extend this Lie algebra to infinite dimensions, which are then reformulated as six-dimensional Lie algebras. For each of these six possible Lie algebras, a system of one-dimensional subalgebras is derived using P. Olver’s method. Group invariant solutions are obtained by performing symmetry reductions under the derived optimal system. The conservation laws of this model are determined using the direct (multiplier) approach. First, the multipliers based on dependent and independent variables are determined and after that, conserved vectors are constructed to correspond to these multipliers. This study presents analytical results in the form of invariant solutions, which are novel due to the nonlinearity of the function <span><math><mrow><mi>Φ</mi><mrow><mo>(</mo><mi>σ</mi><mo>)</mo></mrow></mrow></math></span>. Since very few analytical methods address such nonlinear problems, these solutions offer unique insights. Researchers focusing on numerical solutions can also utilize these results for comparative analysis.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101176"},"PeriodicalIF":0.0,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143935923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A fractional order model of Lymphatic Filariasis and Visceral Leishmaniasis coinfection","authors":"Isaac Kwasi Adu ,&nbsp;Fredrick Asenso Wireko ,&nbsp;Joshua Nii Martey ,&nbsp;Joshua Kiddy K. Asamoah","doi":"10.1016/j.padiff.2025.101204","DOIUrl":"10.1016/j.padiff.2025.101204","url":null,"abstract":"<div><div>Lymphatic filariasis and visceral leishmaniasis are parasitic diseases that cause serious public health issues, especially in tropical and subtropical areas. Effective disease control requires an understanding of their co-infection dynamics. In this study, we construct a fractional-order model to analyze the transmission patterns of lymphatic filariasis and visceral leishmaniasis co-infection. The existence and uniqueness of the model’s solution were confirmed by using the fixed point theory; in addition, the model was proven to be positive and bounded. The stability of the fractional coinfection model is proven using the Hyers–Ulam and Hyers–Ulam–Rassias stability procedures. Sensitivity analysis was conducted using the Latin hypercube sampling technique and partial rank correlation coefficient with 10,000 runs using the reproduction number for lymphatic filariasis and visceral leishmaniasis as the response functions per time. It was observed that the parameters that had a significant influence on the spread of the diseases were <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span>, thus, the biting rates of mosquitoes and sandflies respectively, the progression rate of lymphatic filariasis in mosquitoes <span><math><msub><mrow><mi>b</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>, the progression rate of visceral leishmaniasis in sandflies <span><math><msub><mrow><mi>b</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span>, the progression rate of lymphatic filariasis in humans <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> and the progression rate of visceral leishmaniasis in humans and reservoirs <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span>. Therefore, policymakers are encouraged to focus on reducing the occurrence of these parameters and also use these results as a guide in developing control strategies to mitigate the spread of both disease in the population. We also observed that memory significantly impacts the dynamics of the population’s transmission patterns of lymphatic filariasis and visceral leishmaniasis co-infection.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101204"},"PeriodicalIF":0.0,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143935924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence of ground state solutions for a class of bi-non-local Kirchhoff-type problems with variable exponents","authors":"Hind Bouaam ,&nbsp;Mohamed El Ouaarabi ,&nbsp;Said Melliani ,&nbsp;Maria Alessandra Ragusa","doi":"10.1016/j.padiff.2025.101201","DOIUrl":"10.1016/j.padiff.2025.101201","url":null,"abstract":"<div><div>Our goal in this work is to investigate the existence of ground state solutions, i.e., solutions with the least energy, for a bi-nonlocal Kirchhoff-type problem with variable exponents on compact Riemannian manifolds. Using a minimization argument combined with a quantitative deformation lemma and Brouwer degree theory, we establish the existence of solutions for the problem under consideration.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101201"},"PeriodicalIF":0.0,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143948221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A better iterative algorithm for fixed-point problem in Banach spaces with application","authors":"Wakeel Ahmed ,&nbsp;Shahid Zaman ,&nbsp;Tamseela Ashraf ,&nbsp;Asma Raza","doi":"10.1016/j.padiff.2025.101175","DOIUrl":"10.1016/j.padiff.2025.101175","url":null,"abstract":"<div><div>In this research article, we explore convergence results within the framework of Banach spaces by focusing on a specific iterative scheme, namely the T-iterative algorithm (TIA). Utilizing the Chatterjea–Suzuki-C (CSC) condition, we establish both strong and weak convergence. To validate the efficacy of our proposed iterative schemes, we conduct numerical experiments using MATLAB R2021a, demonstrating that our approach achieves a faster rate of convergence compared to existing methods. Furthermore, we give a clear example of complete mappings that satisfy the CSC condition whose fixed point is unique. As a practical application, we apply the main results to solve functional and fractional differential equations (FDEs), illustrating the broader applicability of our findings.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101175"},"PeriodicalIF":0.0,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143935922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solution of nonlinear telegraph equation with discontinuities along the transmission line using meshless collocation method","authors":"Muhammad Asif ,&nbsp;Tabassum Gul ,&nbsp;Muhammad Bilal Riaz ,&nbsp;Faisal Bilal","doi":"10.1016/j.padiff.2025.101219","DOIUrl":"10.1016/j.padiff.2025.101219","url":null,"abstract":"<div><div>In this paper, we present a novel hybrid numerical technique combining radial basis functions (RBFs) and the finite difference method (FDM) for solving the one-dimensional telegraph interface model (TIM). The presence of interfaces or discontinuities along the transmission line requires additional boundary or interface conditions to accurately describe the voltage and current behaviors at these junctions. Our method incorporates these interface conditions, approximating spatial partial derivatives using RBFs and time derivatives using FDM. To validate our approach, we applied it to several benchmark linear and nonlinear TIMs. For linear models, the resulting algebraic system is solved using Gauss elimination, while for nonlinear models, we employed the quasi-Newton method to linearize the nonlinear terms. We evaluated the method’s performance by calculating the maximum absolute errors (MAEs) and root mean square errors (RMSEs) for different grid points (GPs). Additionally, we compared the true and estimate solutions through three dimensional (3D)graphs. The numerical results show that our technique provides simple implementation, quick convergence, and outstanding accuracy for both linear and nonlinear models. This hybrid approach proves to be a highly effective and reliable tool for solving telegraph interface problems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101219"},"PeriodicalIF":0.0,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143935921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An optimal control analysis of HIV-Visceral Leishmaniasis co-infection model","authors":"Ibrahim M. Elmojtaba","doi":"10.1016/j.padiff.2025.101216","DOIUrl":"10.1016/j.padiff.2025.101216","url":null,"abstract":"<div><div>In this paper, we develop and analyze a novel mathematical model that captures the co-infection dynamics of HIV/AIDS and Visceral Leishmaniasis (VL) in a population where a reservoir host is present—marking the first study to explicitly incorporate reservoir-mediated transmission into HIV-VL interactions. Our analysis reveals that reducing the basic reproduction number below unity does not guarantee disease eradication due to the occurrence of backward bifurcation, highlighting the complex nature of disease persistence. Through global sensitivity analysis, we identify the sandfly biting rate as the most influential factor driving VL transmission, while the natural death rate of sandflies emerges as the most critical parameter in curbing disease spread. Based on these insights, we implement optimal control strategies tailored to the most sensitive parameters, demonstrating effective pathways to mitigate the burden of both infections in the presence of a reservoir host.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101216"},"PeriodicalIF":0.0,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143941960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analyzing coupled wave dynamics in elastic waveguides with height variations: Modeling and insights","authors":"Muhammad Afzal ,&nbsp;Taha Aziz","doi":"10.1016/j.padiff.2025.101208","DOIUrl":"10.1016/j.padiff.2025.101208","url":null,"abstract":"<div><div>This study employs a combined mode matching technique and Galerkin approach to analyze fluid–structure coupled wave interactions a an elastic plate bounded waveguide containing height variation. The dynamical response of plate coupled with the acoustics govern higher order derivative involving boundary value problem. The associated eigenfunctions are non-orthogonal and the system underlies non-Sturm–Liouville system. The Galerkin approach is adopted to model the vibrational response of an elastic plate, while the continuity conditions at the fluid–structure interface are applied to get linear algebraic systems which are truncated and solved numerically. Results confirm power conservation, with reflected and transmitted powers summing to unity across all frequencies. For structure-borne modes, transmission dominates at lower frequencies but fluctuates near cut-on frequencies, while reflection dominates fluid-borne modes due to impedance mismatch. The model’s accuracy is validated by adherence to power conservation and agreement with the tailored-Galerkin method, establishing a reliable framework for analyzing wave energy propagation in coupled systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101208"},"PeriodicalIF":0.0,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143935854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}