Partial Differential Equations in Applied Mathematics最新文献

{"title":"Insights into HIV/AIDS transmission dynamics and control in Indonesia — A mathematical modelling study","authors":"Afeez Abidemi ,&nbsp;Fatmawati ,&nbsp;Cicik Alfiniyah ,&nbsp;Windarto ,&nbsp;Farai Nyabadza ,&nbsp;Muhamad Hifzhudin Noor Aziz","doi":"10.1016/j.padiff.2025.101185","DOIUrl":"10.1016/j.padiff.2025.101185","url":null,"abstract":"<div><div>This paper presented a new deterministic compartmental model of the dynamics of human immunodeficiency virus (HIV) and acquired immunodeficiency syndrome (AIDS). The model included mother-to-child transmission, the effect of treatment delay through saturated treatment, and screening for early case detection. We obtained the effective reproduction number, <span><math><msub><mrow><mi>ℛ</mi></mrow><mrow><mi>e</mi></mrow></msub></math></span>, for the model with the help of the next-generation matrix method. A closer look at the model’s qualitative parts showed that it can reach unique disease-free and endemic equilibrium points when treatment delay is not present. We showed that the disease-free equilibrium is globally asymptotically stable when <span><math><msub><mrow><mi>ℛ</mi></mrow><mrow><mi>e</mi></mrow></msub></math></span> is less than one and unstable when <span><math><msub><mrow><mi>ℛ</mi></mrow><mrow><mi>e</mi></mrow></msub></math></span> is greater than one by making use of Lyapunov function. On the other hand, the endemic equilibrium is globally asymptotically stable when <span><math><msub><mrow><mi>ℛ</mi></mrow><mrow><mi>e</mi></mrow></msub></math></span> is greater than one. We further confronted the model with real data from Indonesia’s annual AIDS cases to obtain more realistic quantitative results. Global sensitivity analysis was carried out to identify the model parameters that most influence the transmission dynamics of HIV/AIDS in the community. We also conducted numerical simulations to illustrate the effects of the three key aspects of HIV/AIDS transmission dynamics which were factored into the model. We discovered that stepping up screening for case detection, treatment, and preventing mother-to-child HIV transmission could potentially prevent thousands of HIV/AIDS cases and AIDS-related deaths in Indonesia by 2029.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101185"},"PeriodicalIF":0.0,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874037","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":"Solitary wave solutions with stability, bifurcation, sensitivity and chaotic analysis of the (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation using beta derivative","authors":"Saikh Shahjahan Miah ,&nbsp;M. Ali Akar ,&nbsp;Kamruzzaman Khan","doi":"10.1016/j.padiff.2025.101192","DOIUrl":"10.1016/j.padiff.2025.101192","url":null,"abstract":"<div><div>The space-time fractional Yu-Toda-Sasa-Fukuyama equation (YTSFE) is widely used to describe elastic quasi-plane waves in a two-layer fluid system, characterizing the behavior of the interface between two immiscible fluid layers of differing densities, relevant to interfacial wave dynamics in such systems. In this work, we explore solitary wave solutions to the (3+1)-dimensional space-time fractional YTSFE and analyze in detail using the extended modified auxiliary equation mapping technique. We construct a variety of solitary wave solutions to this equation, including trigonometric, rational, and hybrid solutions. The solutions include a range of waveforms such as kink, anti-kink, general, and plane-type solitons, which hold numerous applications in physical sciences and engineering. The solutions of this work have been compared with existing results, and new solutions have been identified. The effect of fractional order derivative on the soliton has been shown graphically. The stability, bifurcation, chaotic, and sensitivity analysis of the dynamical system of the governing model have been assessed. The graphical representations of the solutions are provided in 2D, 3D, and contour formats, using MATLAB with appropriately selected parameter values. The method proves to be effective and efficient for investigating nonlinear integrable equations, confirming its potential for addressing the space-time fractional YTSFE.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101192"},"PeriodicalIF":0.0,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143891780","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":"Modeling the spatiotemporal dynamic heterogeneity of pre-synthetic stage breast cancer tumor-immune interactions","authors":"Kennedy Mensah ,&nbsp;Joseph Abeiku Ackora-Prah ,&nbsp;Dominic Otoo ,&nbsp;Atta Kwame Gyamfi","doi":"10.1016/j.padiff.2025.101200","DOIUrl":"10.1016/j.padiff.2025.101200","url":null,"abstract":"<div><div>Breast cancer remains a leading cause of mortality among women worldwide. While metastatic-stage cancer has no cure, understanding the spatiotemporal dynamics of tumor-immune interactions at the pre-synthetic stage is essential for developing effective immunotherapies. Recent advances in cancer modeling emphasize the need to incorporate both spatial and temporal dynamics for accurate simulations. This study presents a continuum model that ensures biological well-posedness. The steady state of the spatially homogeneous model exhibits stability but becomes unstable when spatial effects are incorporated. We performed a parameter sweep analysis to identify stability regions, revealing a critical threshold near <span><math><mrow><msub><mrow><mi>η</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≈</mo><mn>0</mn><mo>.</mo><mn>04</mn></mrow></math></span> where the system transitions from instability to stability. Additionally, the boundaries near <span><math><mrow><msub><mrow><mi>α</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≈</mo><mn>0</mn><mo>.</mo><mn>2</mn></mrow></math></span> and <span><math><mrow><msub><mrow><mi>η</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>≈</mo><mn>0</mn><mo>.</mo><mn>3</mn></mrow></math></span> show the most significant sensitivity to stability changes. By employing an explicit finite difference scheme, our simulations demonstrate spatially heterogeneous interactions among tumor cells, NK cells, and cytokines, with NK cells being most effective near the tumor. This suggests active immune recruitment in response to cancer progression. The spatiotemporal dynamics observed in our model are consistent with findings from existing studies, and the temporal behavior aligns with established patterns of immune-tumor interactions, further validating the robustness of our approach. Further analysis shows that higher per-capita growth rates <span><math><mrow><mo>(</mo><mi>ω</mi><mo>)</mo></mrow></math></span> of tumor cells correlate with rapid proliferation, aligning with their direct influence on tumor growth. This study provides valuable insights into spatial and temporal mechanisms of tumor-immune interactions, offering a foundation for optimizing immunotherapy strategies.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101200"},"PeriodicalIF":0.0,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869723","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 solving Caputo and Riemann–Liouville types of sequential fractional differential equations with boundary conditions using an accurate scheme","authors":"Nazek A. Obeidat,&nbsp;Mahmoud S. Rawashdeh,&nbsp;Omar M. Ababneh","doi":"10.1016/j.padiff.2025.101174","DOIUrl":"10.1016/j.padiff.2025.101174","url":null,"abstract":"<div><div>Due to its significance in every branch of science and engineering today, it is crucial to solve sequential fractional differential equations (SFDEs). In this research work, we study some unique theories on fractional calculus. We present significant relationships among well-known fractional derivative operators and leverage these relationships to create novel approaches to the solution of linear sequential fractional differential equations (LSFDE) with constant coefficients. We use a reliable technique called the Adomian decomposition natural method (ADNM), which combines Adomian decomposition and the natural transform method. The ADNM was then modified to find exact and approximate solutions to fractional partial differential equations (FPDEs) with boundary conditions (B.C.s). The study demonstrates the effectiveness of this technique since it is convenient to implement and provides accurate results. This comprehensive method provides valuable knowledge for scholars and scientists in the science and engineering fields.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101174"},"PeriodicalIF":0.0,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878916","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 nonlinear mathematical analysis of nanoparticle's velocity, temperature and concentration in magnetohydrodynamic convective flow","authors":"Rajendran Nalini ,&nbsp;Athimoolam Meena ,&nbsp;Lakshmanan Rajendran ,&nbsp;Mohammad Izadi","doi":"10.1016/j.padiff.2025.101193","DOIUrl":"10.1016/j.padiff.2025.101193","url":null,"abstract":"<div><div>The mathematical model of chemical processes and heat radiation impacts on the MHD flow of nanofluid is discussed. This model employs nonlinear differential equations, including a nonlinear component associated with combined convection and chemical processes. The changes in temperature, concentration, and velocity caused by thermal factors are examined in this article. In the magnetohydrodynamic flow of copper-water nanofluid, we compute the Nusselt and Sherwood numbers and the skin friction. Our calculations take into consideration both viscosity and ohmic dissipation. This theoretical analysis is conducted for the first time in MHD flow problems using the analytical method (J. Phys. Chem. C 2023, 127, 24, 11,517–11,525) (Rajendran-Joy method) and numerical calculations (Scilab). This analytical result is compared with the numerical result to determine their efficiency and accuracy. Also, the Local Nusselt and Sherwood numbers and skin friction coefficient for various parameters are discussed and compared with the numerical result. The graphs and tables show how different factors affect temperature, concentration, and velocity. A sensitivity analysis of parameters on velocity is also discussed.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101193"},"PeriodicalIF":0.0,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869722","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":"Non-local operator as a mathematical tool to improve the modeling of water pollution phenomena in environmental science: A spatio-temporal approach","authors":"Pasquini Fotsing Soh ,&nbsp;Mathew Kinyanjui ,&nbsp;David Malonza ,&nbsp;Roy Kiogora","doi":"10.1016/j.padiff.2025.101161","DOIUrl":"10.1016/j.padiff.2025.101161","url":null,"abstract":"<div><div>This paper aims to develop a fractional order mathematical model addressing water pollution dynamics. The model is designed to elucidate the effect of pollutants and propose effective strategies for mitigating their spread in various water bodies such as rivers, lakes, oceans, or streams. Firstly, we formulate and analyze a nonlinear ordinary differential equations model that integrates a fractional derivative to capture the memory effect of pollutants in water. We initiate the analysis by establishing the existence of a unique positive and bounded solution. We then compute the basic reproduction number, which dictates the global dynamics of the model. Furthermore, we rigorously demonstrate the existence of a unique pollution-free equilibrium and the endemic equilibrium, and prove their global stability under appropriate assumptions on the basic reproduction number. Additionally, we conduct a global sensitivity analysis of the basic reproduction number to assess the variability in model predictions. Secondly, we enrich this initial model by extending it to a fractional partial differential system, incorporating spatial variables and diffusion terms to elucidate the transmission dynamics of pollutants in a spatially uniform environment. We establish the existence of a unique positive and bounded solution, along with the global stability of both pollution-free and endemic equilibria. To complement our theoretical findings, we perform numerical simulations using finite difference techniques and implemented via MATLAB.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101161"},"PeriodicalIF":0.0,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869725","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 mathematical framework for analyzing co-infection of COVID-19 with lung cancer","authors":"Md. Abdul Hye ,&nbsp;Md. Haider Ali Biswas ,&nbsp;Mohammed Forhad Uddin","doi":"10.1016/j.padiff.2025.101195","DOIUrl":"10.1016/j.padiff.2025.101195","url":null,"abstract":"<div><div>This study introduces a novel mathematical framework to explore the complex relationship between COVID-19 and lung cancer, addressing a critical gap in the existing literature. While various co-infection models have been discussed, no prior work has focused explicitly on the mathematical modeling of COVID-19 and lung cancer co-infection, positioning this research as pioneering. The dynamical model incorporates sub-models to analyze two distinct scenarios: one focusing exclusively on lung cancer and the other on COVID-19. The basic reproduction number determines stability conditions for the disease-free and endemic equilibriums. The model also integrates intervention strategies, including lung cancer preventive measures and COVID-19-specific treatments, to evaluate their impact on co-infection dynamics. Stability analysis and numerical simulations identify critical factors influencing the severity and progression of the co-infection, highlighting the substantial role of lung cancer prevention in reducing COVID-19 co-infections. The results underscore the importance of targeted interventions in managing co-infections effectively. This framework provides valuable insights for researchers and healthcare professionals as a comprehensive tool for understanding co-infection dynamics. By addressing the complexities of COVID-19 and lung cancer co-infection, this study goes beyond previous efforts, offering actionable strategies and advancing the understanding of this critical public health issue.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101195"},"PeriodicalIF":0.0,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143838026","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":"Hopf bifurcation and stability analysis for a delayed prey-predator model subject to a strong Allee effect in the prey species","authors":"Shaimaa A.A. Ahmed ,&nbsp;Waleed A.I. Elmorsi","doi":"10.1016/j.padiff.2025.101199","DOIUrl":"10.1016/j.padiff.2025.101199","url":null,"abstract":"<div><div>This study considers the linear stability of a prey-predator model including time delays under a strong Allee effect among prey species. We drive and analyze the corresponding characteristic transcendental equation, demonstrating the presence of Hopf bifurcation at the positive equilibrium point. We applied normal form approach and center manifold theorem to determine the Hopf bifurcation direction and the stability of the bifurcating periodic solution. A numerical example was ultimately introduced to demonstrate the effectiveness of the theoretical analysis.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101199"},"PeriodicalIF":0.0,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143850156","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":"Enhanced analytical solutions of coupled conformable Gross-Pitaevskii equations incorporating external potentials using a residual series method","authors":"Shaher Momani ,&nbsp;Rawya Al-Deiakeh ,&nbsp;Shrideh Al-Omari ,&nbsp;Mohammed Al-Smadi","doi":"10.1016/j.padiff.2025.101177","DOIUrl":"10.1016/j.padiff.2025.101177","url":null,"abstract":"<div><div>This work concerns the construction of approximate analytical solutions for the nonlinear complex conformable Gross-Pitaevskii equations with an external potential using the residual series method in conformable sense. This technique combines the flexibility of residual error function and generalized multivariable power series, utilizing time-dependent conformable derivatives. By minimizing the residual error, solitary wave solutions in a subtle pattern are generated. Further, convergence analysis is provided to illustrate the theoretical framework of our scheme in handling the proposed nonlinear models. Therefore, for practical computation, several naturalistic applications for Bose-Einstein condensates involving zero trapping, periodic boxes, optical lattices, and harmonic potentials are examined. Additionally, numerical computations and graphical representations are provided to verify the correctness and accuracy of the tested applications. Moreover, the dynamic behaviors of wave soliton solutions are captured at different parameters. These solutions demonstrate the effectiveness of the method and its ease of use in solving many complex nonlinear partial differential equations arising in quantum optics, quantum gases, quantum fluids, and other states of quantum mechanics.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101177"},"PeriodicalIF":0.0,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143855993","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":"Numerical investigation of a fractional order differential human papillomavirus model using time delay neural network","authors":"Dostdar Ali ,&nbsp;Faqir shah ,&nbsp;Asadullah ,&nbsp;Shumaila Javeed ,&nbsp;Ume Ayesha ,&nbsp;Barno Sayfutdinovna Abdullaeva ,&nbsp;Manish Gupta ,&nbsp;Nainaru Tarakaramu","doi":"10.1016/j.padiff.2025.101196","DOIUrl":"10.1016/j.padiff.2025.101196","url":null,"abstract":"<div><div>The objective of this study is to find the numerical results of a fractional order-dynamics model of the Human-papillomavirus (HPV) using time-delayed neural networks (TDNNs) in conjunction with the innovative Levenberg-Marquardt backpropagation (LMB) technique, referred to as TDNNs-LMB. The TDNNs-LMB procedure is carried out using training, validation, and testing data. The fractional-order dynamics model of HPV is analyzed for four distinct cases of fractional-order. In order to address the fractional-order HPV model, the dataset is partitioned into three segments with a split of 70 % allocated for training, 15 % set aside for validation, and another 15 % reserved for testing. A reference solution is established for the comparison of the results produced by the proposed neural network technique with the existing solutions of the HPV fractional model. The absolute error (AE) plots are provided to assess the accuracy and precision of the HPV fractional order-model. The obtained numerical solutions of the HPV model are evaluated in terms of mean square-error (MSE). The efficiency, reliability, and effectiveness of the TDNNs-LMB procedure are demonstrated through numerical performance metrics, including, fitting curves, correlation, state transitions (STs), error histograms (EHs), and MSE.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"14 ","pages":"Article 101196"},"PeriodicalIF":0.0,"publicationDate":"2025-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143855992","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}