Nurushofa, Zuroidah Zeni (2017) Simulasi dan analisa kestabilan model matematika dinamika persebaran kasus perokok / Zuroidah Zeni Nurushofa. Diploma thesis, Universitas Negeri Malang.
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ABSTRACT Nurushofa Zuroidah Zeni. 2017. Simulation and Stability Analysis of Mathematics Dynamics Model on The Spread of Smoker Cases. Thesis Mathematics Department Faculty of Mathematics and Natural Science State University of Malang. Advisor (I) Dr. Rustanto Rahardi M. Si. Keywords Smoker Dynamics Simulation Stability Analysis Mathematical Modeling The continuous number of smokers increases the number of individuals suffering from cigarette diseases thus finding a solution to this problem should be immediately done. One of them is by constructing a mathematical model of the number of smokers so that the dynamics of the number of smokers can be observed. In this thesis it has been discussed mathematical model of the dynamics of the spread of smokers. The population is divided into subpopulations of potential smokers (P) active smokers (S) temporary stop smokers (Q_t) and permanent stop smokers (Q_t). In the first model the interaction occurs between potential smokers and active smokers. In addition individuals in the sub-population stop smokers come from the smoker sub-population. Based on the analysis of the model there are two equilibrium points i.e. smoking free equilibrium (E_0) and smoking present equilibrium (E_1). Using the theorem it can be concluded that the equilibrium point E_0 with E_0 (P S Q_t) is asymptotic stable locally. The second equilibrium point E_1 with E_1 (P S 12310 Q_t 12311 ) is also asymptotic stable locally. From the model analysis we obtain two fixed points for smoker free point stable when R_0 1 while fixed point endemic smoker stable moment R_0 1. In the present-smoking simulation tests were performed using two different R_0 values and the results showed that the greater the R_0 value the smoker and stop smoker population increased. As for the sub-potential smokers the population will decrease. Vice versa the smaller the value of R_0 then the potential population of smokers will increase. As for the population of smokers and population stop smoker the population will decrease.
| Item Type: | Thesis (Diploma) |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Fakultas Matematika dan IPA (FMIPA) > Departemen Matematika (MAT) > S1 Matematika |
| Depositing User: | library UM |
| Date Deposited: | 19 Oct 2017 04:29 |
| Last Modified: | 09 Sep 2017 03:00 |
| URI: | http://repository.um.ac.id/id/eprint/17519 |
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