Sagar R. Khirsariya, Snehal Rao, Jignesh P. Chauhan
The present study examines a semi-analytical method known as the Fractional Residual Power Series Method for obtaining solutions to the non-linear, time-fractional Kawahara and modified Kawahara equations. These equations are fifth-order, non-linear partial differential equations that arise in the context of shallow water waves. The analytical process and findings are compared with those obtained from the well-known Variational Iteration Method (VIM) and Homotopy Perturbation Method (HPM). The results obtained from the Fractional Residual Power Series Method are found to be more efficient, reliable, and easier to implement compared to other analytical and semi-analytical methods.
{"title":"Solution of fractional modified Kawahara equation: a semi-analytic approach","authors":"Sagar R. Khirsariya, Snehal Rao, Jignesh P. Chauhan","doi":"10.5206/mase/16369","DOIUrl":"https://doi.org/10.5206/mase/16369","url":null,"abstract":"The present study examines a semi-analytical method known as the Fractional Residual Power Series Method for obtaining solutions to the non-linear, time-fractional Kawahara and modified Kawahara equations. These equations are fifth-order, non-linear partial differential equations that arise in the context of shallow water waves. The analytical process and findings are compared with those obtained from the well-known Variational Iteration Method (VIM) and Homotopy Perturbation Method (HPM). The results obtained from the Fractional Residual Power Series Method are found to be more efficient, reliable, and easier to implement compared to other analytical and semi-analytical methods.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138947280","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}
Under the Dirichlet boundary setting, Aryal and Karki (2022) studied an inverse problem of recovering an initial temperature profile from known temperature measurements at a fixed location of a one-dimensional body and at linearly growing finitely many later times within a bounded interval. This paper studies the problem under the Neumann boundary conditions. That is, under this boundary setting, we suitably select a fixed location x0 on the body of length π and construct finitely many times tk, k = 1, 2, 3, . . . , n that grow linearly with k and are in [0, T] such that from the temperature measurements taken at x0 and at these n times, we recover the initial temperature profile f(x) with a desired accuracy, provided f is in a suitable subset of L2[0, π].
在 Dirichlet 边界条件下，Aryal 和 Karki（2022 年）研究了一个逆问题，即从一维物体固定位置的已知温度测量值，以及在有界区间内线性增长的有限多次以后的温度测量值，恢复初始温度曲线。本文研究的是诺伊曼边界条件下的问题。也就是说，在这种边界条件下，我们在长度为 π 的体上适当选择一个固定位置 x0，并构建有限多次 tk, k = 1, 2, 3, ., n，这些时间与 k 呈线性增长，且位于 [0, T] 中，这样，只要 f 位于 L2[0, π] 的一个合适子集中，我们就能根据在 x0 和这 n 个时间测量到的温度，以理想的精度恢复初始温度曲线 f(x)。
{"title":"Recovery of an initial temperature of a one-dimensional body from finite time-observations","authors":"Ramesh Karki, Chava Shawn, Young You","doi":"10.5206/mase/16723","DOIUrl":"https://doi.org/10.5206/mase/16723","url":null,"abstract":"Under the Dirichlet boundary setting, Aryal and Karki (2022) studied an inverse problem of recovering an initial temperature profile from known temperature measurements at a fixed location of a one-dimensional body and at linearly growing finitely many later times within a bounded interval. This paper studies the problem under the Neumann boundary conditions. That is, under this boundary setting, we suitably select a fixed location x0 on the body of length π and construct finitely many times tk, k = 1, 2, 3, . . . , n that grow linearly with k and are in [0, T] such that from the temperature measurements taken at x0 and at these n times, we recover the initial temperature profile f(x) with a desired accuracy, provided f is in a suitable subset of L2[0, π].","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"111 39","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138958399","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}
Taye Faniran, M. O. Adewole, Catherine Chirouze, Antoine Perasso, Raluca Eftimie
Methicillin-Resistant Staphylococcus Aureus (MRSA) infection can occur alongside or following COVID-19, which is a concern in healthcare settings. The effectiveness of antiviral treatments for COVID-19 depends on a functioning immune response, but antibiotics used for bacterial infections like MRSA can disrupt the immune response and reduce the effectiveness of antiviral treatments. The emergence of MRSA due to excessive antibiotic usage has led to the widespread use of vancomycin as an alternative treatment. Immunomodulatory antibiotics like azithromycin may also be considered. To study the dynamics of these coinfections, a multiscale model was developed. Parameter estimation and sensitivity analysis were performed, revealing influential parameters affecting the reproduction number. Numerical simulations showed that methicillin may increase the population of co-infected cells, while azithromycin can improve the host immune response but has limited impact on MRSA proliferation. Increased efficacy of vancomycin can lead to MRSA eradication. Combination of immunomodulatory antibiotics and vancomycin has minimal effect on co-infected cell population, but increased vancomycin efficacy can reduce coinfection severity. This study emphasizes the importance of continuous research, surveillance, and the development of effective strategies to combat the complexities of COVID-19 and MRSA coinfection.
{"title":"Multiscale modeling approach to assess the impact of antibiotic treatment for COVID-19 on MRSA transmission and alternative immunotherapy treatment options","authors":"Taye Faniran, M. O. Adewole, Catherine Chirouze, Antoine Perasso, Raluca Eftimie","doi":"10.5206/mase/16685","DOIUrl":"https://doi.org/10.5206/mase/16685","url":null,"abstract":"Methicillin-Resistant Staphylococcus Aureus (MRSA) infection can occur alongside or following COVID-19, which is a concern in healthcare settings. The effectiveness of antiviral treatments for COVID-19 depends on a functioning immune response, but antibiotics used for bacterial infections like MRSA can disrupt the immune response and reduce the effectiveness of antiviral treatments. The emergence of MRSA due to excessive antibiotic usage has led to the widespread use of vancomycin as an alternative treatment. Immunomodulatory antibiotics like azithromycin may also be considered. To study the dynamics of these coinfections, a multiscale model was developed. Parameter estimation and sensitivity analysis were performed, revealing influential parameters affecting the reproduction number. Numerical simulations showed that methicillin may increase the population of co-infected cells, while azithromycin can improve the host immune response but has limited impact on MRSA proliferation. Increased efficacy of vancomycin can lead to MRSA eradication. Combination of immunomodulatory antibiotics and vancomycin has minimal effect on co-infected cell population, but increased vancomycin efficacy can reduce coinfection severity. This study emphasizes the importance of continuous research, surveillance, and the development of effective strategies to combat the complexities of COVID-19 and MRSA coinfection.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"17 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138967406","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}
Biological invasion has become an important element of global changes. In this paper, we use a reaction-diffusion system to discuss the minimal invasion speed of two competing species in the homogeneous environment. The general condition for the minimum invasion speed is obtained by applying the theory of propagation dynamics. Then the explicit conditions are derived by constructing upper solutions. The analytical results are corroborated by simulations of the considered reaction-diffusion system. Our results reveal the impact of the diffusion rate, growth rate, competitiveness of the species, as well as the carrying capacity of the environment, on the invasion speed, which provides an effective method for preventing biological invasion and controlling existing biological invasion.
{"title":"The minimal invasion speed of two competing species in homogeneous environment","authors":"Xu Li, Tingting Zhang, Qiming Zhang","doi":"10.5206/mase/16801","DOIUrl":"https://doi.org/10.5206/mase/16801","url":null,"abstract":"Biological invasion has become an important element of global changes. In this paper, we use a reaction-diffusion system to discuss the minimal invasion speed of two competing species in the homogeneous environment. The general condition for the minimum invasion speed is obtained by applying the theory of propagation dynamics. Then the explicit conditions are derived by constructing upper solutions. The analytical results are corroborated by simulations of the considered reaction-diffusion system. Our results reveal the impact of the diffusion rate, growth rate, competitiveness of the species, as well as the carrying capacity of the environment, on the invasion speed, which provides an effective method for preventing biological invasion and controlling existing biological invasion.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139233195","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}
This paper discusses a mathematical model describing the formation of tuberculosis(TB) granulomas. The main purpose is to analyze the change trend of Mtb and immune cells in different stages after Mtb invaded the host. The theoretical analysis indicates that the existence and global stability of bacteria-free equilibrium and bacteria-present equilibrium under different conditions. In addition, the sensitivity analysis is performed on the parameters, which determines the parameters that have the greatest impact on Mtb invading the host. The stage of no infection, the latent TB infection(LTBIs) and active TB corresponding to the clearance, survival or growth and reproduction of Mtb are displayed by the numerical simulations. The results suggest that whether the individuals infected with Mtb will be progressed to the active TB depends on the immune system of individuals.
{"title":"Analysis of a simple mathematical model describing tuberculous granuloma","authors":"Yuqi Jin, Hui Cao, Xiaxia Xu","doi":"10.5206/mase/16678","DOIUrl":"https://doi.org/10.5206/mase/16678","url":null,"abstract":"This paper discusses a mathematical model describing the formation of tuberculosis(TB) granulomas. The main purpose is to analyze the change trend of Mtb and immune cells in different stages after Mtb invaded the host. The theoretical analysis indicates that the existence and global stability of bacteria-free equilibrium and bacteria-present equilibrium under different conditions. In addition, the sensitivity analysis is performed on the parameters, which determines the parameters that have the greatest impact on Mtb invading the host. The stage of no infection, the latent TB infection(LTBIs) and active TB corresponding to the clearance, survival or growth and reproduction of Mtb are displayed by the numerical simulations. The results suggest that whether the individuals infected with Mtb will be progressed to the active TB depends on the immune system of individuals.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"358 17","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135392986","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}
Chagas disease is a zoonosis caused by the protozoan parasite Trypanosoma cruzi and transmitted by a broad range of blood-sucking triatomine species. Recently, it is recognized that the parasite can also be transmitted by host ingestion. In this paper, we propose a Chagas disease model incorporating two transmission routes of biting-defecation and host predation between vectors and hosts with Holling II functional response. The basic reproduction number R_v of triatomine population and basic reproduction numbers R_0 of disease population are derived analytically, and it is shown that they are insufficient to serve as threshold quantities to determine dynamics of the model. Our results have revealed the phenomenon of bistability, with backward and forward bifurcations. Specifically, if R_v>1, the dynamic is rather simple, namely, the disease-free equilibrium is globally asymptotically stable as R_0<1 and a unique endemic equilibrium is globally asymptotically stable as R_0>1. However, if R_v<1, there exists a backward bifurcation with one unstable and one stable positive vector equilibria, and bistability phenomenon occurs, revealing that different initial conditions may lead to disease extinction or persistence even if the corresponding R_0>1. In conclusion, predation transmission in general reduces the risk of Chagas disease, whilst it makes the complexity of Chagas disease transmission, requiring an integrated strategy for the prevention and control of Chagas disease.
{"title":"Assessing the impact of host predation with Holling II response on the transmission of Chagas disease","authors":"Jiahao Jiang, Daozhou Gao, Jiao Jiang, Xiaotian Wu","doi":"10.5206/mase/16743","DOIUrl":"https://doi.org/10.5206/mase/16743","url":null,"abstract":"Chagas disease is a zoonosis caused by the protozoan parasite Trypanosoma cruzi and transmitted by a broad range of blood-sucking triatomine species. Recently, it is recognized that the parasite can also be transmitted by host ingestion. In this paper, we propose a Chagas disease model incorporating two transmission routes of biting-defecation and host predation between vectors and hosts with Holling II functional response. The basic reproduction number R_v of triatomine population and basic reproduction numbers R_0 of disease population are derived analytically, and it is shown that they are insufficient to serve as threshold quantities to determine dynamics of the model. Our results have revealed the phenomenon of bistability, with backward and forward bifurcations. Specifically, if R_v>1, the dynamic is rather simple, namely, the disease-free equilibrium is globally asymptotically stable as R_0<1 and a unique endemic equilibrium is globally asymptotically stable as R_0>1. However, if R_v<1, there exists a backward bifurcation with one unstable and one stable positive vector equilibria, and bistability phenomenon occurs, revealing that different initial conditions may lead to disease extinction or persistence even if the corresponding R_0>1. In conclusion, predation transmission in general reduces the risk of Chagas disease, whilst it makes the complexity of Chagas disease transmission, requiring an integrated strategy for the prevention and control of Chagas disease.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"32 25","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135390992","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}
SARS-CoV-2 can survive in different environments and remain infectious for several days, which presents challenges to eliminating infectious diseases. It encourages researchers to study the effects of SARS CoV-2 on the environment. In this paper, we formulate an epidemic model for SARS-CoV-2, which focuses on the transmission of the virus under environmental conditions. Two distributed delays are introduced to describe the probability of the exposed and infected individuals in different infection periods based on the transmission of the virus in the environment. Th positivity and boundedness of solutions of model are derived. The basic reproduction number threshold theory is established and the results demonstrate that the persistence of COVID-19 depends on the basic reproduction number. Numerical simulations are presented to verify the theoretical results. Some measures are proposed to control and eliminate COVID-19 infectious diseases.
{"title":"Dynamical analysis of a COVID-19 model with human-to-human and environment-to-human transmissions and distributed delays","authors":"Jie Xu, Yayuan Lei, TARIQ ABDULLAH, Gang Huang","doi":"10.5206/mase/16681","DOIUrl":"https://doi.org/10.5206/mase/16681","url":null,"abstract":"SARS-CoV-2 can survive in different environments and remain infectious for several days, which presents challenges to eliminating infectious diseases. It encourages researchers to study the effects of SARS CoV-2 on the environment. In this paper, we formulate an epidemic model for SARS-CoV-2, which focuses on the transmission of the virus under environmental conditions. Two distributed delays are introduced to describe the probability of the exposed and infected individuals in different infection periods based on the transmission of the virus in the environment. Th positivity and boundedness of solutions of model are derived. The basic reproduction number threshold theory is established and the results demonstrate that the persistence of COVID-19 depends on the basic reproduction number. Numerical simulations are presented to verify the theoretical results. Some measures are proposed to control and eliminate COVID-19 infectious diseases.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135803896","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}
Most biological populations reside in landscapes that consist of many different patches of different quality. Different species differ in their movement behavior, habitat preference and growth rates. Historically, mathematical models for population dynamics have made many simplifying assumptions, such as a single patch or homogeneous landscapes. Recent models have begun to implement landscape heterogeneity and individual movement characteristics, but many of those are based on logistic growth and linear analysis of the zero state. We consider a two-patch model with more general growth functions that can include Allee effects. We prove the existence of steady states and classify their qualitative behavior. In some special cases, we explicitly calculate their stability and use these results to give conditions for when the system exhibits bistability, i.e., the coexistence of locally stable states. We also study bifurcations with respect to the size of habitat patches and give conditions for forward and backward bifurcations.
{"title":"Steady-state dynamics in a two-patch population model with and without Allee effect","authors":"Laurence Ketchemen Tchouaga, Frithjof Lutscher","doi":"10.5206/mase/16474","DOIUrl":"https://doi.org/10.5206/mase/16474","url":null,"abstract":"Most biological populations reside in landscapes that consist of many different patches of different quality. Different species differ in their movement behavior, habitat preference and growth rates. Historically, mathematical models for population dynamics have made many simplifying assumptions, such as a single patch or homogeneous landscapes. Recent models have begun to implement landscape heterogeneity and individual movement characteristics, but many of those are based on logistic growth and linear analysis of the zero state. We consider a two-patch model with more general growth functions that can include Allee effects. We prove the existence of steady states and classify their qualitative behavior. In some special cases, we explicitly calculate their stability and use these results to give conditions for when the system exhibits bistability, i.e., the coexistence of locally stable states. We also study bifurcations with respect to the size of habitat patches and give conditions for forward and backward bifurcations.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136061376","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}
Rough set concept is a methodology of information processing for relational databases. It is a unique uncertainty mathematics topic closely connected to fuzzy set theory. When the rough set is combined with neutrosophic set theory, an effective tool for working with indeterminacy arises. In this study, we defined a multi-valued rough neutrosophic set and a multi-valued rough neutrosophic matrix. Using separation measures, we introduced a new approach for a multi-valued neutrosophic with a rough structure. We consider the problem of determining the condition of dengue-affected patients in a specific hospital. Using this method, we create a multi-valued rough neutrosophic decision matrix that clearly displays the relationship between patient conditions and symptoms. We can determine which one has a serious condition by solving this problem and presenting it on the graph.
{"title":"Application of multi-valued rough neutrosophic set and matrix in multi-criteria decision-making","authors":"Donbosco Jeni Seles Martina, Ganesan Deepa","doi":"10.5206/mase/16636","DOIUrl":"https://doi.org/10.5206/mase/16636","url":null,"abstract":"Rough set concept is a methodology of information processing for relational databases. It is a unique uncertainty mathematics topic closely connected to fuzzy set theory. When the rough set is combined with neutrosophic set theory, an effective tool for working with indeterminacy arises. In this study, we defined a multi-valued rough neutrosophic set and a multi-valued rough neutrosophic matrix. Using separation measures, we introduced a new approach for a multi-valued neutrosophic with a rough structure. We consider the problem of determining the condition of dengue-affected patients in a specific hospital. Using this method, we create a multi-valued rough neutrosophic decision matrix that clearly displays the relationship between patient conditions and symptoms. We can determine which one has a serious condition by solving this problem and presenting it on the graph.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136059922","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}
Xinfu Chen, Xin Lai, Cong Qin, Y. Qi, Yajing Zhang
We study a reaction-diffusion system which models the pre-mixed isothermal autocatalytic chemical reaction of order m (m > 1) between two chemical species, a reactant A and an auto-catalyst B, A + m B --> (m+1) B, and a linear decay B -->C, where C is an inert product. The special case of m = 2 is the much studied Gray-Scott model, but without feeding. We prove existence of multiple traveling waves which have distinctive number of local maximaor peaks. It shows a new and very distinctive feature of Gray-Scott type of models in generating rich and structurally different traveling pulses than related models in literature such as isothermal autocatalysis without decay, or a bio-reactor model with isothermal autocatalysis of order m + 1 with m-th order of decay.
我们研究了一个反应扩散系统，该系统模拟了两种化学物质，反应物a和自催化剂B, a + m B—> (m+1) B和线性衰变B—>C之间的m (m >)级预混合等温自催化化学反应，其中C是惰性产物。m = 2的特殊情况是研究得很多的Gray-Scott模型，但没有喂食。证明了具有不同数目的局部极大峰的多个行波的存在性。与文献中的无衰变等温自催化、m + 1阶等温自催化、m阶衰变的生物反应器模型相比，Gray-Scott型模型在产生丰富且结构不同的行脉冲方面表现出了一个新的非常鲜明的特点。
{"title":"Multiple-peak traveling waves of the Gray-Scott model","authors":"Xinfu Chen, Xin Lai, Cong Qin, Y. Qi, Yajing Zhang","doi":"10.5206/mase/16513","DOIUrl":"https://doi.org/10.5206/mase/16513","url":null,"abstract":"We study a reaction-diffusion system which models the pre-mixed isothermal autocatalytic chemical reaction of order m (m > 1) between two chemical species, a reactant A and an auto-catalyst B, A + m B --> (m+1) B, and a linear decay B -->C, where C is an inert product. The special case of m = 2 is the much studied Gray-Scott model, but without feeding. We prove existence of multiple traveling waves which have distinctive number of local maximaor peaks. It shows a new and very distinctive feature of Gray-Scott type of models in generating rich and structurally different traveling pulses than related models in literature such as isothermal autocatalysis without decay, or a bio-reactor model with isothermal autocatalysis of order m + 1 with m-th order of decay.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44139249","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}
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