Pub Date : 2019-08-09DOI: 10.20473/CONMATHA.V1I1.14772
S. Suherman, F. Fatmawati, Cicik Alfiniyah
Ebola disease is one of an infectious disease caused by a virus. Ebola disease can be transmitted through direct contact with Ebola’s patient, infected medical equipment, and contact with the deceased individual. The purpose of this paper is to analyze the stability of equilibriums and to apply the optimal control of treatment on the mathematical model of the spread of Ebola with medical treatment. Model without control has two equilibria, namely non-endemic equilibrium (E0) and endemic equilibrium (E1) The existence of endemic equilibrium and local stability depends on the basic reproduction number (R0). The non-endemic equilibrium is locally asymptotically stable if R0 < 1 and endemic equilibrium tend to asymptotically stable if R0 >1 . The problem of optimal control is then solved by Pontryagin’s Maximum Principle. From the numerical simulation result, it is found that the control is effective to minimize the number of the infected human population and the number of the infected human with medical treatment population compare without control.
{"title":"Analisis Kestabilan dan Kontrol Optimal Model Matematika Penyebaran Penyakit Ebola dengan Penanganan Medis","authors":"S. Suherman, F. Fatmawati, Cicik Alfiniyah","doi":"10.20473/CONMATHA.V1I1.14772","DOIUrl":"https://doi.org/10.20473/CONMATHA.V1I1.14772","url":null,"abstract":"Ebola disease is one of an infectious disease caused by a virus. Ebola disease can be transmitted through direct contact with Ebola’s patient, infected medical equipment, and contact with the deceased individual. The purpose of this paper is to analyze the stability of equilibriums and to apply the optimal control of treatment on the mathematical model of the spread of Ebola with medical treatment. Model without control has two equilibria, namely non-endemic equilibrium (E0) and endemic equilibrium (E1) The existence of endemic equilibrium and local stability depends on the basic reproduction number (R0). The non-endemic equilibrium is locally asymptotically stable if R0 < 1 and endemic equilibrium tend to asymptotically stable if R0 >1 . The problem of optimal control is then solved by Pontryagin’s Maximum Principle. From the numerical simulation result, it is found that the control is effective to minimize the number of the infected human population and the number of the infected human with medical treatment population compare without control.","PeriodicalId":119993,"journal":{"name":"Contemporary Mathematics and Applications (ConMathA)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133553647","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 aims to solve Open Vehicle Routing Problem using Firefly Algorithm. Open Vehicle Routing Problem (OVRP) is a variant of Vehicle Routing Problem (VRP) where vehicles used to serve customers do not return to the depot after serving the last customer on each route. The steps of the Firefly Algorithm to handle OVRP are data input and initialization parameters, generating the initial population for each firefly, sorting population sources, calculating the value of the objective function and light intensity, comparing the intensity of light, performing movement, setting the best fireflies as g-best, doing random movement in the best fireflies as long as the maximum number of iterations has not been met. The program used to complete OVRP using the Firefly Algorithm is Borland C ++ and implemented in 3 case examples, namely small data with 18 customers, moderate data with 50 customers, and large data with 100 customers with the best total mileage of 211, 344 , 970.62, and 2531.83. The results obtained from the program output indicate that the more the number of iterations and the number of fireflies, then the results of the objective function (total mileage) obtained tend to be better so that these parameters affect the value of the objective function. While the absorption coefficient value (g) does not give effect to the value of the objective function.
{"title":"Penerapan Algoritma Kunang-Kunang pada Open Vehicle Routing Problem (OVRP)","authors":"Ihda Septiyafi, Herry Suprajitno, Asri Bekti Pratiwi","doi":"10.20473/conmatha.v1i1.14774","DOIUrl":"https://doi.org/10.20473/conmatha.v1i1.14774","url":null,"abstract":"This paper aims to solve Open Vehicle Routing Problem using Firefly Algorithm. Open Vehicle Routing Problem (OVRP) is a variant of Vehicle Routing Problem (VRP) where vehicles used to serve customers do not return to the depot after serving the last customer on each route. The steps of the Firefly Algorithm to handle OVRP are data input and initialization parameters, generating the initial population for each firefly, sorting population sources, calculating the value of the objective function and light intensity, comparing the intensity of light, performing movement, setting the best fireflies as g-best, doing random movement in the best fireflies as long as the maximum number of iterations has not been met. The program used to complete OVRP using the Firefly Algorithm is Borland C ++ and implemented in 3 case examples, namely small data with 18 customers, moderate data with 50 customers, and large data with 100 customers with the best total mileage of 211, 344 , 970.62, and 2531.83. The results obtained from the program output indicate that the more the number of iterations and the number of fireflies, then the results of the objective function (total mileage) obtained tend to be better so that these parameters affect the value of the objective function. While the absorption coefficient value (g) does not give effect to the value of the objective function.","PeriodicalId":119993,"journal":{"name":"Contemporary Mathematics and Applications (ConMathA)","volume":"21 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113957071","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}
Pub Date : 2019-08-09DOI: 10.20473/CONMATHA.V1I1.14773
A. B. Pratiwi, Nur Faiza, Edi Winarko
The aim of this research is to solve Uncapacitated Facility Location Problem (UFLP) using Cuckoo Search Algorithm (CSA). UFLP involves n locations and facilities to minimize the sum of the fixed setup costs and serving costs of m customers. In this problem, it is assumed that the built facilities have no limitations in serving customers, all request from each customers only require on facility, and one location only provides one facility. The purpose of the UFLP is to minimize the total cost of building facilities and customer service costs. CSA is an algorithm inspired by the parasitic nature of some cuckoo species that lay their eggs in other host birds nests. The Cuckoo Search Algorithm (CSA) application program for resolving Uncapacitated Facility Location Problems (UFLP) was made by using Borland C ++ programming language implemented in two sample cases namely small data and big data. Small data contains 10 locations and 15 customers, while big data consists 50 locations and 50 customers. From the computational results, it was found that higher number of nests and iterations lead to minimum total costs. Smaller value of pa brought to better solution of UFLP.
{"title":"Penerapan Cuckoo Search Algorithm (CSA) untuk Menyelesaikan Uncapacitated Facility Location Problem (UFLP)","authors":"A. B. Pratiwi, Nur Faiza, Edi Winarko","doi":"10.20473/CONMATHA.V1I1.14773","DOIUrl":"https://doi.org/10.20473/CONMATHA.V1I1.14773","url":null,"abstract":"The aim of this research is to solve Uncapacitated Facility Location Problem (UFLP) using Cuckoo Search Algorithm (CSA). UFLP involves n locations and facilities to minimize the sum of the fixed setup costs and serving costs of m customers. In this problem, it is assumed that the built facilities have no limitations in serving customers, all request from each customers only require on facility, and one location only provides one facility. The purpose of the UFLP is to minimize the total cost of building facilities and customer service costs. CSA is an algorithm inspired by the parasitic nature of some cuckoo species that lay their eggs in other host birds nests. The Cuckoo Search Algorithm (CSA) application program for resolving Uncapacitated Facility Location Problems (UFLP) was made by using Borland C ++ programming language implemented in two sample cases namely small data and big data. Small data contains 10 locations and 15 customers, while big data consists 50 locations and 50 customers. From the computational results, it was found that higher number of nests and iterations lead to minimum total costs. Smaller value of pa brought to better solution of UFLP.","PeriodicalId":119993,"journal":{"name":"Contemporary Mathematics and Applications (ConMathA)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132743352","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}
Pub Date : 2019-08-09DOI: 10.20473/CONMATHA.V1I1.14775
W AniesYulinda, L. Novia, Melati Tegarina, Nurul Chamidah
Life expectancy can be used to evaluate the government's performance for improving the welfare of the population in the health sector. Life expectancy is closely related to infant mortality rate. Theoretically, decreasing of infant mortality rate will cause increasing of life expectancy. A statistical method that can be used to model life expectancy is nonparametric regression model based on least square spline estimator. This method provides high flexibility to accommodate pattern of data by using smoothing technique. The best estimated model is order one spline model with one knot based on minimum generalized cross validation (GCV) value of 0.607. Each increasing of one infant mortality rate unit will cause decreasing of life expectancy of 0.2314 for infant mortality rate less than 27, and of 0.0666 for infant mortality rate more than and equals to 27. In addition, based on mean square error (MSE) of 0.492 and R2value of 76.59% for nonparametric model approach compared with MSE of 0.634 and R2 value of 71.8% for parametric model approach, we conclude that the use of nonparametric model approach based on least square spline estimator is better than that of parametric model approach.
{"title":"ANALISIS PENGARUH ANGKA KEMATIAN BAYI TERHADAP ANGKA HARAPAN HIDUP DI PROVINSI JAWA TIMUR BERDASARKAN ESTIMATOR LEAST SQUARE SPINE","authors":"W AniesYulinda, L. Novia, Melati Tegarina, Nurul Chamidah","doi":"10.20473/CONMATHA.V1I1.14775","DOIUrl":"https://doi.org/10.20473/CONMATHA.V1I1.14775","url":null,"abstract":"Life expectancy can be used to evaluate the government's performance for improving the welfare of the population in the health sector. Life expectancy is closely related to infant mortality rate. Theoretically, decreasing of infant mortality rate will cause increasing of life expectancy. A statistical method that can be used to model life expectancy is nonparametric regression model based on least square spline estimator. This method provides high flexibility to accommodate pattern of data by using smoothing technique. The best estimated model is order one spline model with one knot based on minimum generalized cross validation (GCV) value of 0.607. Each increasing of one infant mortality rate unit will cause decreasing of life expectancy of 0.2314 for infant mortality rate less than 27, and of 0.0666 for infant mortality rate more than and equals to 27. In addition, based on mean square error (MSE) of 0.492 and R2value of 76.59% for nonparametric model approach compared with MSE of 0.634 and R2 value of 71.8% for parametric model approach, we conclude that the use of nonparametric model approach based on least square spline estimator is better than that of parametric model approach.","PeriodicalId":119993,"journal":{"name":"Contemporary Mathematics and Applications (ConMathA)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122649097","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}
Research on the local adjacency metric dimension has not been found in all operations of the graph, one of them is comb product graph. The purpose of this research was to determine the local adjacency metric dimension of k-comb product graph and level comb product graph between any connected graph G and H. In this research graph G and graph H such as cycle graph, complete graph, path graph, and star graph. K-comb product graph between any graph G and H denoted by GokH. While level k comb product graph between any graph G and H denoted by GokH.In this research, local adjacency metric dimension of GokSm graph only dependent to multiplication of the cardinality of V(G) and many of k value, while GokKm graph and GokCm graph is dependent to dominating number of G and multiplication of the cardinality of V(G), many of k value, and local adjacency metric dimension of Km graph or Cm graph. And then, local adjacency metric dimension of GokSm graph only dependent to the cardinality of V(Gok-1Sm), while GokKm graph and GokCm graph is dependent to dominating number of G and multiplication of the local adjacency metric dimension of Km graph or Cm graph with cardinality of V(Gok-1Km) or V(Gok-1Cm).
{"title":"DIMENSI METRIK KETETANGGAAN LOKAL GRAF HASIL OPERASI k-COMB","authors":"Fryda Arum Pratama, Lili Susilowati, Moh. Imam Utoyo","doi":"10.20473/CONMATHA.V1I1.14771","DOIUrl":"https://doi.org/10.20473/CONMATHA.V1I1.14771","url":null,"abstract":"Research on the local adjacency metric dimension has not been found in all operations of the graph, one of them is comb product graph. The purpose of this research was to determine the local adjacency metric dimension of k-comb product graph and level comb product graph between any connected graph G and H. In this research graph G and graph H such as cycle graph, complete graph, path graph, and star graph. K-comb product graph between any graph G and H denoted by GokH. While level k comb product graph between any graph G and H denoted by GokH.In this research, local adjacency metric dimension of GokSm graph only dependent to multiplication of the cardinality of V(G) and many of k value, while GokKm graph and GokCm graph is dependent to dominating number of G and multiplication of the cardinality of V(G), many of k value, and local adjacency metric dimension of Km graph or Cm graph. And then, local adjacency metric dimension of GokSm graph only dependent to the cardinality of V(Gok-1Sm), while GokKm graph and GokCm graph is dependent to dominating number of G and multiplication of the local adjacency metric dimension of Km graph or Cm graph with cardinality of V(Gok-1Km) or V(Gok-1Cm). ","PeriodicalId":119993,"journal":{"name":"Contemporary Mathematics and Applications (ConMathA)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117099738","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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