Mathematical Methods in the Applied Sciences最新文献

{"title":"Unveiling Activated NK Cell Dynamics in Salmonella Typhi Infection Under Optimum Double-Drug (Azithromycin and IFN−γ) Therapy: An Immuno-Mathematical Model Analysis","authors":"Shu Wang, Amit Kumar Roy","doi":"10.1002/mma.11193","DOIUrl":"https://doi.org/10.1002/mma.11193","url":null,"abstract":"<div>\u0000 \u0000 <p>This article presents a four-dimensional nonlinear immuno-mathematical model to elucidate the crucial role of activated natural killer (NK) cells during the interaction between <i>Salmonella</i> Typhi (<i>S</i>. Typhi) bacteria and macrophages. Analytically, we have demonstrated the direct involvement of NK cell-mediated immune responses through Interferon - \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>γ</mi>\u0000 </mrow>\u0000 <annotation>$$ gamma $$</annotation>\u0000 </semantics></math> (\u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>I</mi>\u0000 <mi>F</mi>\u0000 <mi>N</mi>\u0000 <mo>−</mo>\u0000 <mi>γ</mi>\u0000 </mrow>\u0000 <annotation>$$ IFN-gamma $$</annotation>\u0000 </semantics></math>) signaling in the necessary conditions for disease persistence. The stability criteria for disease-free and endemic equilibria are theoretically validated using the basic reproduction number (\u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>ℛ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {mathcal{R}}_0 $$</annotation>\u0000 </semantics></math>) and the Routh-Hurwitz criterion. Our system exhibits a transcritical bifurcation at \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>ℛ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$$ {mathcal{R}}_0=1 $$</annotation>\u0000 </semantics></math>, indicating changes in the stability of the disease-free and endemic equilibria. We have also investigated the effects of a dual-drug regimen (Azithromycin and \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>I</mi>\u0000 <mi>F</mi>\u0000 <mi>N</mi>\u0000 <mo>−</mo>\u0000 <mi>γ</mi>\u0000 </mrow>\u0000 <annotation>$$ IFN-gamma $$</annotation>\u0000 </semantics></math>) by introducing two surrogate control parameters into our model, utilizing optimal control theory. The derived optimal drug dosage pair offers a cost-effective and efficient treatment strategy. For model calibration via numerical simulations, we have collected some parameter values from certain published mouse model studies and also performed sensitivity analysis for \u0000<span></span><math>\u0000 <semantic","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14505-14520"},"PeriodicalIF":1.8,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence of Weak Solutions for a Degenerate Goursat-Type Linear Problem","authors":"Olimpio Hiroshi Miyagaki,&nbsp;Carlos Alberto Reyes Peña,&nbsp;Rodrigo da Silva Rodrigues","doi":"10.1002/mma.11181","DOIUrl":"https://doi.org/10.1002/mma.11181","url":null,"abstract":"<p>For a generalization of the Gellerstedt operator with mixed-type Dirichlet boundary conditions to a suitable Tricomi domain, we prove the existence and uniqueness of weak solutions of the linear problem and for a generalization of this problem. The classical method introduced by Didenko, which study the energy integral argument, will be used to prove estimates for a specific Tricomi domain.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14334-14341"},"PeriodicalIF":1.8,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.11181","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global Solvability of 3D Inhomogeneous Nematic Liquid Crystal Flows With Only Bounded Density in Critical Besov Space","authors":"Dongxiang Chen,&nbsp;Xingyu Liang,&nbsp;Xia Ye","doi":"10.1002/mma.11169","DOIUrl":"https://doi.org/10.1002/mma.11169","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This paper is devoted to proving the global existence and uniqueness of weak solutions to the three-dimensional inhomogeneous incompressible nematic liquid crystal flows. The results hold under the conditions that the initial density lies in the bounded function space with a positive lower bound, the initial velocity is sufficiently small in the critical Besov space \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mover&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;˙&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℝ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {dot{B}}_{2,1}&amp;amp;#x0005E;{frac{1}{2}}left({mathbb{R}}&amp;amp;#x0005E;3right) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, and the gradient of the initial molecular orientation is also small enough in the same critical Besov space \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mover&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;˙&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;m","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14159-14193"},"PeriodicalIF":1.8,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145013280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global Stability and Optimal Control in a Dengue Model With Fractional-Order Transmission and Recovery Process","authors":"Tahajuddin Sk,&nbsp;Kaushik Bal,&nbsp;Santosh Biswas,&nbsp;Tridip Sardar","doi":"10.1002/mma.11191","DOIUrl":"https://doi.org/10.1002/mma.11191","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;The current manuscript introduces a single-strain dengue model developed from stochastic processes incorporating fractional-order transmission and recovery. The fractional derivative has been introduced within the context of transmission and recovery process, displaying characteristics similar to tempered fractional (\u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ TF $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;) derivatives. It has been established that under certain condition, a function's \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ TF $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; derivatives are proportional to the function itself. Applying the following observation, we examined the stability of several steady-state solutions, such as disease-free and endemic states, in light of this newly formulated model, using the reproduction number (\u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {R}_0 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;). In addition, the precise range of epidemiological parameters for the fractional-order model was determined by calibrating weekly registered dengue incidence in the San Juan municipality of Puerto Rico, from April 9, 2010, to April 2, 2011. We performed a global sensitivity analysis method to measure the influence of key model parameters (along with the fractional-order coefficient) on total dengue cases and the basic reproduction number (\u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {R}_0 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;) using a Monte Carlo-based partial rank correlation coefficient (PRCC). Moreover, we formulated a fractional-order model with fractional control to assess the effectiveness of different interventions, such as reducing the recruitment rate of mosquito breeding, controlling adult vectors, and providing individual protection. Also, we established the existence of a solution for the fractional-order optimal control problem. Finally, the numerical experiment illustrates that policymakers should place importance on the fractional-order transmission and recovery parameters that capture the","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14459-14487"},"PeriodicalIF":1.8,"publicationDate":"2025-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145013114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Normalized Ground State Solutions to HLS Upper Critical Choquard Equation With Mass Critical or Supercritical and Sobolev Critical Growth","authors":"Jianlun Liu,&nbsp;Ziheng Zhang,&nbsp;Hong-Rui Sun","doi":"10.1002/mma.11177","DOIUrl":"https://doi.org/10.1002/mma.11177","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This paper is concerned with the following HLS upper critical Choquard equation with mass critical or supercritical and Sobolev critical growth \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mtable&gt;\u0000 &lt;mtr&gt;\u0000 &lt;mtd&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;Δ&lt;/mi&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;4&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;∗&lt;/mo&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;5&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14276-14289"},"PeriodicalIF":1.8,"publicationDate":"2025-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145013211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lie Symmetry Analysis, Optimal Systems, and Conservation Laws for Two-Dimensional Compressible Euler Equations With Chaplygin Gas","authors":"Dia Zeidan,&nbsp;Sandhya Maurya,&nbsp;Manoj Pandey","doi":"10.1002/mma.11185","DOIUrl":"https://doi.org/10.1002/mma.11185","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we employ Lie classical symmetries to analyze the two-dimensional isentropic Euler equations system for Chaplygin gas. Adjoint operators play an essential part in deriving an optimal system of subalgebras. Introducing a novel approach, we present a method for constructing a two-dimensional optimal system through strategic adjoint actions which is using the largest chain of removal operators. By employing the vector fields obtained from the optimal system, we efficiently transform the governing model into a collection of ordinary differential equations. Consequently, we attain group invariant solutions and elucidate their graphical behavior. Moreover, we obtain conservation laws for the governing model by utilizing it is nonlinear self-adjoint properties and employing the direct multiplier method.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14385-14400"},"PeriodicalIF":1.8,"publicationDate":"2025-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145013304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Insights on Stochastic Dynamics for Transmission of Monkeypox: Biological and Probabilistic Behavior","authors":"Ghaus ur Rahman,&nbsp;Olena Tymoshenko,&nbsp;Giulia Di Nunno","doi":"10.1002/mma.11180","DOIUrl":"https://doi.org/10.1002/mma.11180","url":null,"abstract":"<div>\u0000 \u0000 <p>The transmission of monkeypox is studied using a stochastic model taking into account the biological aspects, the contact mechanisms and the demographic factors, together with the intrinsic uncertainties. Our results provide insight into the interaction between stochasticity and biological elements in the dynamics of monkeypox transmission. The rigorous mathematical analysis determines threshold parameters for disease persistence. For the proposed model, the existence of a unique global almost sure nonnegative solution is proven. Conditions leading to disease extinction are established. Asymptotic properties of the model are investigated such as the speed of transmission.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14316-14333"},"PeriodicalIF":1.8,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145013265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spatiotemporal Patterns and Bifurcation Analysis With Degenerate Cases in a Charge Transfer Model","authors":"Meihua Wei,&nbsp;Zhiwei Tang,&nbsp;Gaihui Guo","doi":"10.1002/mma.11187","DOIUrl":"https://doi.org/10.1002/mma.11187","url":null,"abstract":"<div>\u0000 \u0000 <p>A priori estimates and the nonexistence of nonconstant positive steady-state solutions of a charge transfer model are established. Steady-state and Hopf bifurcations are carried out in detail, especially under the degenerate conditions such as invalid simple eigenvalue condition or crossing condition. It is shown that the steady-state solutions under the violated simple eigenvalue are characterized by a coupling of two eigenfunctions, and the bifurcation direction from simple eigenvalue is supercritical or subcritical. Meanwhile, there is no nonconstant steady-state solution under the degenerate case of violated crossing condition. In addition, whether the transversality condition in Hopf bifurcation is true or not, instead of the center manifold theory, we apply the Lyapunov-Schmidt reduction method and the singularity theory to illustrate the existence and stability of periodic solutions as well as the bifurcation diagrams. But it is proved that the usual pitchfork Hopf bifurcation is changed to the transcritical bifurcation through the invalid transversality condition. Finally, some numerical simulations allow us to identify the influence of external current on the predicted dynamics. The novel results on the effect of degeneracy obtained in this paper shall complement classical theories and enrich numerical examples in the existing work.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14413-14431"},"PeriodicalIF":1.8,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145013264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamical Analysis of an HIV Infection Model Including Quiescent Cells and Immune Response","authors":"Ibrahim Nali,&nbsp;Attila Dénes,&nbsp;Abdessamad Tridane,&nbsp;Xueyong Zhou","doi":"10.1002/mma.11179","DOIUrl":"https://doi.org/10.1002/mma.11179","url":null,"abstract":"&lt;p&gt;This research gives a thorough examination of a human immunodeficiency virus (HIV) infection model that includes quiescent cells and immune response dynamics in the host. The model, represented by a system of ordinary differential equations, captures the complex interaction between the host's immune response and viral infection. The study focuses on the model's fundamental aspects, such as equilibrium analysis, computing the basic reproduction number \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℛ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {mathcal{R}}_0 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, stability analysis, bifurcation phenomena, numerical simulations, and sensitivity analysis. The analysis reveals both an infection equilibrium, which indicates the persistence of the illness, and an infection-free equilibrium, which represents disease control possibilities. Applying matrix-theoretical approaches, stability analysis proved that the infection-free equilibrium is both locally and globally stable for \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℛ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {mathcal{R}}_0&amp;amp;lt;1 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. For the situation of \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℛ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {mathcal{R}}_0&amp;amp;gt;1 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, the infection equilibrium is locally asymptotically stable via the Routh-Hurwitz criterion. We also studied the uniform persistence of the infection, demonstrating that the infection remains present above a positive threshold under certain conditions. The study also found a transcritical forward-type bifurcation at \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℛ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14301-14315"},"PeriodicalIF":1.8,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.11179","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145013315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Software Belief Reliability Growth Model Considering Testing Coverage Based on Liu Process","authors":"Zhe Liu,&nbsp;Rui Kang","doi":"10.1002/mma.11178","DOIUrl":"https://doi.org/10.1002/mma.11178","url":null,"abstract":"<div>\u0000 \u0000 <p>Software has been increasingly important in many critical systems. To measure the growth of software reliability during testing phases, several software reliability growth models (SRGMs) have been investigated. Different from hardwares, softwares' failure mechanisms follow the basic rules of logic, behavior, and psychology rather than physical laws. Consequently, software testing phase embodies lots of epistemic uncertainties, which are not suitable to be modeled by probability theory-based SRGMs. In addition, fuzzy theory-based SRGMs may give counterintuitive results. Confronted with these, we proposed a software belief reliability growth model (SBRGM) under the framework of uncertainty theory which is a new mathematics system to deal with epistemic uncertainties. However, testing coverage, a key factor in software testing, has not been considered in SBRGM. Therefore, a novel SBRGM considering testing coverage, named SBRGM with testing coverage (TCSBRGM), is proposed in this paper. Based on belief reliability theory, several essential belief reliability indexes for software such as belief reliability and belief reliable time are considered. Unknown parameters in the proposed TCSBRGM are estimated. Finally, real data analysis using two real-world software testing data is carried out to compare the performance of our proposed model with some representative SRGMs. The results exhibit that the proposed model gives a better fitting and predictive performance.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14290-14300"},"PeriodicalIF":1.8,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145013317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}