{"title":"解决癌症患者人类免疫缺陷病毒系统问题的新型径向基和西格玛神经网络组合","authors":"Zulqurnain Sabir, Sahar Dirani, Sara Bou Saleh, Mohamad Khaled Mabsout, Adnène Arbi","doi":"10.3390/math12162490","DOIUrl":null,"url":null,"abstract":"The purpose of this work is to design a novel process based on the deep neural network (DNN) process to solve the dynamical human immunodeficiency virus (HIV-1) infection system in cancer patients (HIV-1-ISCP). The dual hidden layer neural network structure using the combination of a radial basis and sigmoid function with twenty and forty neurons is presented for the solution of the nonlinear HIV-1-ISCP. The mathematical form of the model is divided into three classes named cancer population cells (T), healthy cells (H), and infected HIV (I) cells. The validity of the designed novel scheme is proven through the comparison of the results. The optimization is performed using a competent scale conjugate gradient procedure, the correctness of the proposed numerical approach is observed through the reference results, and negligible values of the absolute error are around 10−3 to 10−4. The database numerical solutions are achieved from the Runge–Kutta numerical scheme, and are used further to reduce the mean square error by taking 72% of the data for training, while 14% of the data is taken for testing and substantiations. To authenticate the credibility of this novel procedure, graphical plots using different performances are derived.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"78 1","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Novel Radial Basis and Sigmoid Neural Network Combination to Solve the Human Immunodeficiency Virus System in Cancer Patients\",\"authors\":\"Zulqurnain Sabir, Sahar Dirani, Sara Bou Saleh, Mohamad Khaled Mabsout, Adnène Arbi\",\"doi\":\"10.3390/math12162490\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The purpose of this work is to design a novel process based on the deep neural network (DNN) process to solve the dynamical human immunodeficiency virus (HIV-1) infection system in cancer patients (HIV-1-ISCP). The dual hidden layer neural network structure using the combination of a radial basis and sigmoid function with twenty and forty neurons is presented for the solution of the nonlinear HIV-1-ISCP. The mathematical form of the model is divided into three classes named cancer population cells (T), healthy cells (H), and infected HIV (I) cells. The validity of the designed novel scheme is proven through the comparison of the results. The optimization is performed using a competent scale conjugate gradient procedure, the correctness of the proposed numerical approach is observed through the reference results, and negligible values of the absolute error are around 10−3 to 10−4. The database numerical solutions are achieved from the Runge–Kutta numerical scheme, and are used further to reduce the mean square error by taking 72% of the data for training, while 14% of the data is taken for testing and substantiations. To authenticate the credibility of this novel procedure, graphical plots using different performances are derived.\",\"PeriodicalId\":18303,\"journal\":{\"name\":\"Mathematics\",\"volume\":\"78 1\",\"pages\":\"\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-08-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3390/math12162490\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3390/math12162490","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
A Novel Radial Basis and Sigmoid Neural Network Combination to Solve the Human Immunodeficiency Virus System in Cancer Patients
The purpose of this work is to design a novel process based on the deep neural network (DNN) process to solve the dynamical human immunodeficiency virus (HIV-1) infection system in cancer patients (HIV-1-ISCP). The dual hidden layer neural network structure using the combination of a radial basis and sigmoid function with twenty and forty neurons is presented for the solution of the nonlinear HIV-1-ISCP. The mathematical form of the model is divided into three classes named cancer population cells (T), healthy cells (H), and infected HIV (I) cells. The validity of the designed novel scheme is proven through the comparison of the results. The optimization is performed using a competent scale conjugate gradient procedure, the correctness of the proposed numerical approach is observed through the reference results, and negligible values of the absolute error are around 10−3 to 10−4. The database numerical solutions are achieved from the Runge–Kutta numerical scheme, and are used further to reduce the mean square error by taking 72% of the data for training, while 14% of the data is taken for testing and substantiations. To authenticate the credibility of this novel procedure, graphical plots using different performances are derived.
期刊介绍:
Mathematics (ISSN 2227-7390) is an international, open access journal which provides an advanced forum for studies related to mathematical sciences. It devotes exclusively to the publication of high-quality reviews, regular research papers and short communications in all areas of pure and applied mathematics. Mathematics also publishes timely and thorough survey articles on current trends, new theoretical techniques, novel ideas and new mathematical tools in different branches of mathematics.