M. F. Tabassum, M. Farman, A. Akgul, Sanagou Akram
{"title":"非线性松材枯萎病模型的数学处理:一种进化方法","authors":"M. F. Tabassum, M. Farman, A. Akgul, Sanagou Akram","doi":"10.52280/pujm.2022.540904","DOIUrl":null,"url":null,"abstract":"In human life, the forest plays an important role in safeguarding trees against disease infection. The pine wilt disease is one of the big threats for the forest and the environment. Optimum control theory is about discovering a complex system control rule over a period of time. In this paper Evolutionary Pad¶e Approximation (EPA) scheme has been implemented for the treatment of non-linear pine wilt disease model.\nEvolutionary Pad¶e Approximation scheme transforms the nonlinear pine wilt disease model into optimization problem. Initial conditions are converted into problem constraints and then constraint problem is converted into unconstraint problem by using penalty function. Sufficient parameter settings for EPA have been implemented. The simulations are numerical solutions of the model of pine wilt disease by solving the proven problem of optimization. It is also determined the threshold value for the fundamental reproductive number and the endemic disease balance point of\nthe model. Evolutionary Pad¶e Approximation has provided convergence\nsolution regarding relationship among the different population compartments\nfor diseases equilibrium, it has been observed that the results EPA\nscheme are more reliable and significant when a comparison is drawn with Non-Standard Finite Difference (NSFD) numerical scheme. Finally, EPA\nscheme reduces the infected rates very fast. Further, in a strong contrast\nto NFSD, this technique has eliminated the need to provide step size.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Mathematical Treatment of Nonlinear Pine Wilt Disease Model: An Evolutionary Approach\",\"authors\":\"M. F. Tabassum, M. Farman, A. Akgul, Sanagou Akram\",\"doi\":\"10.52280/pujm.2022.540904\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In human life, the forest plays an important role in safeguarding trees against disease infection. The pine wilt disease is one of the big threats for the forest and the environment. Optimum control theory is about discovering a complex system control rule over a period of time. In this paper Evolutionary Pad¶e Approximation (EPA) scheme has been implemented for the treatment of non-linear pine wilt disease model.\\nEvolutionary Pad¶e Approximation scheme transforms the nonlinear pine wilt disease model into optimization problem. Initial conditions are converted into problem constraints and then constraint problem is converted into unconstraint problem by using penalty function. Sufficient parameter settings for EPA have been implemented. The simulations are numerical solutions of the model of pine wilt disease by solving the proven problem of optimization. It is also determined the threshold value for the fundamental reproductive number and the endemic disease balance point of\\nthe model. Evolutionary Pad¶e Approximation has provided convergence\\nsolution regarding relationship among the different population compartments\\nfor diseases equilibrium, it has been observed that the results EPA\\nscheme are more reliable and significant when a comparison is drawn with Non-Standard Finite Difference (NSFD) numerical scheme. Finally, EPA\\nscheme reduces the infected rates very fast. Further, in a strong contrast\\nto NFSD, this technique has eliminated the need to provide step size.\",\"PeriodicalId\":205373,\"journal\":{\"name\":\"Punjab University Journal of Mathematics\",\"volume\":\"47 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-09-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Punjab University Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.52280/pujm.2022.540904\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Punjab University Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52280/pujm.2022.540904","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Mathematical Treatment of Nonlinear Pine Wilt Disease Model: An Evolutionary Approach
In human life, the forest plays an important role in safeguarding trees against disease infection. The pine wilt disease is one of the big threats for the forest and the environment. Optimum control theory is about discovering a complex system control rule over a period of time. In this paper Evolutionary Pad¶e Approximation (EPA) scheme has been implemented for the treatment of non-linear pine wilt disease model.
Evolutionary Pad¶e Approximation scheme transforms the nonlinear pine wilt disease model into optimization problem. Initial conditions are converted into problem constraints and then constraint problem is converted into unconstraint problem by using penalty function. Sufficient parameter settings for EPA have been implemented. The simulations are numerical solutions of the model of pine wilt disease by solving the proven problem of optimization. It is also determined the threshold value for the fundamental reproductive number and the endemic disease balance point of
the model. Evolutionary Pad¶e Approximation has provided convergence
solution regarding relationship among the different population compartments
for diseases equilibrium, it has been observed that the results EPA
scheme are more reliable and significant when a comparison is drawn with Non-Standard Finite Difference (NSFD) numerical scheme. Finally, EPA
scheme reduces the infected rates very fast. Further, in a strong contrast
to NFSD, this technique has eliminated the need to provide step size.