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<![CDATA[PEMODELAN MATEMATIKA PENYEBARAN PENYAKIT LEPTOSPIROSIS DENGAN PENGARUH TREATMENT ]]>
<![CDATA[Ingrit Ridha Rahayu]]>;
<![CDATA[Muhammad Subhan]]>
<![CDATA[ Journal of Mathematics UNP Vol 7, No 1 (2022): Journal Of Mathematics UNP ]]>
Publisher : <![CDATA[UNIVERSITAS NEGERI PADANG ]]>
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DOI: 10.24036/unpjomath.v7i1.10923
<![CDATA[Leptospirosis is a disease passive from bacteria and affect humans and animals.Leptospirosis is transmitted from human to human, from animal to animal, from animal to human. In this study, we will look for a mathematical model of the spread of Leptospirosis with the effect of treatment. The purpose of this modelling is to determine the spread of Leptospirosis with the effect of treatment, to determine the analysis of the mathematical model of the spread of Leptospirosis with the effect of treatment, and to determine the interpretation of mathematical model of the spread of Leptospirosis with the effect of treatment. This research past by determining the variables, parameters, and assumptions which linked to the problem, so that the mathematical model spread of Leptospirosis disease with the effect of treatment. After that mathematical model of the spread of Leptospirosis disease with the effect of treatment will be analyzed and interpreted. Based on analysis result point out that at a fixed point free disease, where the fixed point free disease is stable.]]>
<![CDATA[Metode Iterasi Prediktor Korektor Jarratt Householder Untuk Penentuan Akar Persamaan Non Linier ]]>
<![CDATA[Yoga Aprila]]>;
<![CDATA[Muhammad Subhan]]>
<![CDATA[ Journal of Mathematics UNP Vol 8, No 1 (2023): Journal Of Mathematics UNP ]]>
Publisher : <![CDATA[UNIVERSITAS NEGERI PADANG ]]>
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DOI: 10.24036/unpjomath.v8i1.13421
<![CDATA[Determining roots of non-linear equation are often problem in mathematics and engineering. In general, these non-linear equations will appear in complex form that make difficult to solve analytically, so assistance of numerical methods is needed to determining the roots. One of the numerical methods that can be used including Newton-Raphson’s Method, Jarratt’s Method, and Householder’s Method. However, the drawback of these methods are their low order of convergence. Predictor Corrector Jarratt-Householder Iterative Method is a method that arises due to the shortcomings of these methods. The purpose of this research is to study how the process of construction of Predictor Corrector Jarratt-Householder Iterative Method , making algorithm, and finding the order of convergence. The numerical simulation test results with several functions show that Predictor Corrector Jarratt-Householder Iterative Method can finds roots faster than Newton-Raphson’s Method, Jarratt's Method, and Householder's Method.]]>
<![CDATA[Penentuan Premi Asuransi Jiwa Berjangka Status Last Survivor Menggunakan Model GFGM-Type II Copula ]]>
<![CDATA[Peni Erawati]]>;
<![CDATA[Muhammad Subhan]]>
<![CDATA[ Journal of Mathematics UNP Vol 7, No 2 (2022): Journal Of Mathematics UNP ]]>
Publisher : <![CDATA[UNIVERSITAS NEGERI PADANG ]]>
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DOI: 10.24036/unpjomath.v7i2.12570
<![CDATA[The last survivor status of term life insurance is multiple life insurance whose benefits are paid by the insurance company to the heirs if all policyholders have died within a predetermined period of time. The risk of death of a married couple is usually assumed to be independent of each other. But in fact there is a relationship between the risk of death for the couple. The method that can be used to determine the premium for married couples with the assumption of independence is the GFGM-Type II Copula method. The purpose of this study is to determine the formulation of the last survivor term life insurance premium using the GFGM-Type II Copula method. The results obtained from this study are the formulation of the last survivor term life insurance premium using the GFGM-Type II Copula method. Based on the simulation results, it is concluded that the last survivor term life insurance premium calculated with the assumption of independence is smaller than using GFGM-Type II copula Copula.]]>
<![CDATA[Model Matematika Interaksi Glukosa-Insulin Dalam Tubuh Penderita Diabetes Tipe 1 ]]>
<![CDATA[Nurma Yenni]]>;
<![CDATA[Muhammad Subhan]]>
<![CDATA[ Journal of Mathematics UNP Vol 7, No 3 (2022): Journal Of Mathematics UNP ]]>
Publisher : <![CDATA[UNIVERSITAS NEGERI PADANG ]]>
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DOI: 10.24036/unpjomath.v7i3.12905
<![CDATA[Diabetes Mellitus (DM) is a metabolic disease caused by a lack of the hormone insulin. This disease is a non-communicable disease that causes death. Diabetes control measures are needed, especially trying to keep blood sugar levels as close to normal as possible. This research is a basic or theoretical research. This study begins by determining the variables, assumptions, and parameters related to the problem so that a mathematical model of the glucose-insulin interaction in the body of type 1 diabetes patients can be formed. one equilibrium point. Then the stability of the equilibrium point is seen based on the eigenvalues of the Jacobi matrix, which shows that all the eigenvalues are negative, so that the equilibrium point of the mathematical model of glucose-insulin interaction in the body of type 1 diabetics is asymotic stable. This shows that diabetes will not disappear from the sufferer's body. The results of the numerical simulation also strengthen the analysis that has been carried out.]]>
<![CDATA[Model Matematika Dinamika Kemiskinan Dengan Pengaruh Konsumsi Alkohol ]]>
<![CDATA[isra miati]]>;
<![CDATA[Muhammad Subhan]]>
<![CDATA[ Journal of Mathematics UNP Vol 8, No 1 (2023): Journal Of Mathematics UNP ]]>
Publisher : <![CDATA[UNIVERSITAS NEGERI PADANG ]]>
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DOI: 10.24036/unpjomath.v8i1.13440
<![CDATA[The problem of poverty is a major development challenge at the global level. Many strategies are implemented to overcome this problem of poverty. However, in overcoming this problem a common problem emerged among poor families, namely related to alcohol consumption. As a result of consuming excessive alcohol will make individuals become alcohol dependent and alcoholics. The aim of this research is to be able to see a mathematical model and the analysis obtained. The method used in this research is descriptive method. Based on the analysis that has been done, one free fixed point is obtained. Next, the stability of the fixed point will be determined, which shows that the free fixed point is stable if γδ+γμ+μσ+μ^2+μ_1 σ+μ_1 δ+μ_1 μ>βσ+βδ+βμ. The simulation results for the free fixed point show that at a certain time the problem will disappear if the rate of individuals from the poor group who are not addicted to alcohol to poor alcohol addicts (β) is reduced and the rate of individuals in the poor group addicted to alcohol in rehabilitation (γ) is increased.]]>
<![CDATA[Sifat-Sifat Matriks Ketetanggaan Pada Graf Petersen ]]>
<![CDATA[Yuco Alsbaldo]]>;
<![CDATA[Muhammad Subhan]]>
<![CDATA[ Journal of Mathematics UNP Vol 6, No 3 (2021): Journal Of Mathematics UNP ]]>
Publisher : <![CDATA[UNIVERSITAS NEGERI PADANG ]]>
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DOI: 10.24036/unpjomath.v6i3.11910
<![CDATA[Graphs are used to represent discrete objects and the relationships between these objects. One of the best known and very popular examples of graphs is Petersen graph.Petersen graph is very popular because of its uniqueness as a counterexample in many places and has many interesting properties. Graphs can beexpressed in the form of a matrix adjacencywhich is denoted. When a graph can be expressed in the form of an adjacency matrix, its determinants and eigenvalues can be determined. This research is a theoretical research through literature study. The purpose of this study is to find out how the properties of the adjacency matrix on a Petersen graph are. The concept that will be discussed in this research is how the properties of the determinants and eigenvalues of the adjacency matrix on the Petersen graph. The result of the research is that the determinant of the adjacency matrix on the Petersen graph is positive with three different eigenvalues and can be diagonalized because the algebraic multiplicity is the same as the geometric multiplicity mA = mG]]>
<![CDATA[Model Matematika Penyebaran Nomophobia ]]>
<![CDATA[Anjely Aunaya Alfatihah]]>;
<![CDATA[Muhammad Subhan]]>
<![CDATA[ Journal of Mathematics UNP Vol 7, No 2 (2022): Journal Of Mathematics UNP ]]>
Publisher : <![CDATA[UNIVERSITAS NEGERI PADANG ]]>
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DOI: 10.24036/unpjomath.v7i2.12690
<![CDATA[Nomophobia is a psychological disease that causes a person to feel dependent on smartphones. In this study, a mathematical model of the spread of nomophobia will be formed. The purpose of the formation of this mathematical model is to provide an overview of the spread of nomophobia. The method used in this study is a descriptive method, namely, analyzing theories regarding the problems discussed. Based on the results of the analysis of the mathematical model of the spread of nomophobia, two fixed points are obtained, namely the disease-free fixed point and the endemic fixed point. Next, the stability of the fixed point will be determined, which shows that the disease-free fixed point is asymptotically stable, while the endemic fixed point is asymptotically stable if βπ>(δ+μ)(γ+μ). The simulation results for the disease-free fixed point show that at a certain time the disease will disappear, while for the endemic fixed point it shows that at a certain time the disease will outbreak if the rate of interaction between susceptible individuals and individuals infected with nomophobia is higher than the rate of individuals who have self-control and individual doing therapy.]]>
<![CDATA[Analisis Stabilitas dan Kontrol Optimal Model Matematika Kecanduan Game Online ]]>
<![CDATA[putri karimah]]>;
<![CDATA[Muhammad Subhan]]>
<![CDATA[ Journal of Mathematics UNP Vol 7, No 3 (2022): Journal Of Mathematics UNP ]]>
Publisher : <![CDATA[UNIVERSITAS NEGERI PADANG ]]>
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DOI: 10.24036/unpjomath.v7i3.12605
<![CDATA[The purpose of this study is to see how the analysis of stability and optimal control of the mathematical model of online game addiction so that the problem of addiction to online games can be resolved in the future. The author conducted a stability analysis of the model equilibrium point where there are two equilibrium points and also obtained the basic reproduction number R_0=(〖(k〗_2+μ)k_1 β+〖(1-k〗_1)(δ+μ)α+〖(1-k〗_1)β(1-γ)k_2)/(〖(k〗_2+μ)(δ+μ) ). By using Pontryagin's maximum principle, optimal control of the control variables is obtained, namely 〖k_1〗^*=min{1,maks(0,1/c_1 (λ_2-λ_3 )S((αI+βP)/N))} dan 〖k_2〗^*=min{1,maks(0,1/c_2 ((λ_2-λ_3 )I+〖(λ〗_3-λ_4)γI))}.The purpose of this study is to see how the analysis of stability and optimal control of the mathematical model of online game addiction so that the problem of addiction to online games can be resolved in the future. The author conducted a stability analysis of the model equilibrium point where there are two equilibrium points and also obtained the basic reproduction number . By using Pontryagin's maximum principle, optimal control of the control variables is obtained, namely dan.]]>
<![CDATA[Model Matematika Produksi Persediaan Dengan Adanya Kerusakan Barang Dan Mempertimbangkan Pengurangan Harga Serta Penundaan Pembayaran ]]>
<![CDATA[Desi Triana Putri]]>;
<![CDATA[Muhammad Subhan]]>
<![CDATA[ Journal of Mathematics UNP Vol 8, No 1 (2023): Journal Of Mathematics UNP ]]>
Publisher : <![CDATA[UNIVERSITAS NEGERI PADANG ]]>
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DOI: 10.24036/unpjomath.v8i1.13441
<![CDATA[The problem about total cost of inventory that is not optimal in a company that produces its own item is something that happen and important to complete. The problem occur because the inventory control applied by the company is not effective.Deteriorating item and allowing price discount are thing that cause the total cost of inventory is not optimal. In generally, payment that made after the item are received by the customer. However the company allowing delay in payment. The purpose of this study is to form a mathematical modelling about total cost inventory is not optimal at company with deteriorating item, price discount and delay in payment. The result of this study are a model of inventory with deteriorating item. The equation for the total cost of inventory obtained by the excistence payment delay period of replenishment item incur interest cost which cause the total cost of inventory to be greater.]]>
<![CDATA[Model Penyebaran Rumor di Media Sosial ]]>
<![CDATA[Tasya Salsabilla Harista]]>;
<![CDATA[Muhammad Subhan]]>
<![CDATA[ Journal of Mathematics UNP Vol 8, No 2 (2023): Journal Of Mathematics UNP ]]>
Publisher : <![CDATA[UNIVERSITAS NEGERI PADANG ]]>
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DOI: 10.24036/unpjomath.v8i2.14515
<![CDATA[Rumors are information that spreads widely without any confirmation of truth and definite facts. One of the media that is used in rumors spreading is social media. The negative impact raised by rumors spreading through social media is the disruption of social stability, economic systems, and politics. The research purpose is to analyze the rumor spreading model on social media. This research is basic research (theoretical) using descriptive methods. The analytical results are obtained of a rumor-free equilibrium point and a rumor spread equilibrium point, each of which is asymptotic stable. The basic reproduction number obtained by the rumor will spread if the rate of movement of the population of individual who never hear the rumor or counter-rumor increases and became a individual who have been exposed to the rumor or counter-rumor.]]>
