Sudradjat Supian

Mathematical Model Of Tuberculosis Transmission With Reccurent Infection And Vaccination

This paper presents a model of tuberculosis transmission with vaccination by explicitely considering the total number of recovered individuals, either from natural recovery or due to vaccination. In this paper the endemic and nonendemic fixed points, basic reproduction number, and vaccination reproduction number are given. Some results regarding the stability of the fixed points and the relation to the basic reproduction numbers are analysed. At the end of this study, the numerical computation presented and it shows that vaccination is capable to reduce the number of laten and infectious populations.

The application of genetic algorithm optimization on quadratic investment portfolio without a risk-free asset under Value-at-Risk

In this paper, we performed the Genetic Algorithm within problems of quadratic investment portfolio without a risk-free asset under Value-at-Risk. The limitation of this study is that the risk of an investment portfolio measured by Value-at-Risk, and each investor has the nature of risk aversion. To solve these problems: First, we established the mean vector and covariance matrix. The second step was to define the vector mean and covariance matrices for the formulation of Value-at-Risk of the investment portfolio. Third, using the mean vector and Value-at-Risk established the model. To complete the optimization problem, we performed the Genetic Algorithm. The results show that the trade-off between risk and expected return does not only depend on the type of investor but also on the size of the investment. The Genetic Algorithm certifies us the robust solution in the optimization problem because of its natural ability to locate the global minimal. Moreover, genetic algorithm can be used as an effective way in numerical completion of the optimization of quadratic investment portfolio. In a realistic investment situation, it has likely more constraints. For example, the restriction on short-selling, is need to be considered.

Numerical Simulation on Solving Three-Dimensional Global Optimization Problems in cooperation of Filled Function and Search Direction

Global optimization problem still becomes an interest due to the challenge of locating the global optimum of nonlinear objective function with multiple local minima. Two challenges on solving global optimization problem are; firstly how to reach the better minimizer from the current minimizer, and secondly how to decide that the obtained minimizer is the desired global minimizer. One of the recent considered deterministic easy applied methods, which concerned in the mentioned problems, is the filled function method. The basic concept of filled function method is to build such an auxiliary function to locate a point with lower function value than the current minimizer. One of the keys to the successfully filled function method is how to decide the search direction to reach and locate a better local minimizer. In this paper, a three-dimensional filled function method and its search direction are introduced. The algorithm is presented and implemented to some benchmark test function. The numerical performance of the method on solving three-dimensional global optimization problems is presented.

Solving Unconstrained Global Optimization Problem Using Parameter Free Filled Function in Cooperation with Jameson Gradient Based Method

Global optimization problem still becomes a challenges due to the problem on locating the global optimum of multimodal function. How to reach the better minimizer from the current minimizer and how to decide that the obtained minimizer is the desired one are both major challenges on solving global optimization problem. Filled function method is one of the recent considered deterministic easy applied methods which concerned to the mentioned problems. The basic concept of filled function method is firstly by minimizing the objective function (first phase) then to build such an auxiliary function which to be minimized (second phase) in order to locate a point with lower function value than the current minimizer of the objective function. In the second phase, a local minimization method can be applied. Newtons method is considered to be fast method on finding the zero of gradient of quadratic function, but may be very expensive or infeasible to determine the Hessian matrix in the case of complex problems. The Jameson gradient based method is the search procedures which avoid the need to store an estimate of the Hessian as well as its inverse and do not require exact line searches. In this paper, an algorithm in cooperation of parameter free filled function method and Jameson gradient method are introduced for solving global optimization problem with two variables. The algorithm is implemented to some benchmark test function. The numerical performance of the method on solving two-dimensional global optimization problems is presented.

Supply and demand analysis for flood insurance by using logistic regression model: case study at Citarum watershed in South Bandung, West Java, Indonesia

Floods have always occurred in the Citarum river basin. The adverse effects caused by floods can cover all their property, including the destruction of houses. The impact due to damage to residential buildings is usually not small. Indeed, each of flooding, the government and several social organizations providing funds to repair the building. But the donations are given very limited, so it cannot cover the entire cost of repair was necessary. The presence of insurance products for property damage caused by the floods is considered very important. However, if its presence is also considered necessary by the public or not? In this paper, the factors that affect the supply and demand of insurance product for damaged building due to floods are analyzed. The method used in this analysis is the ordinal logistic regression. Based on the analysis that the factors that affect the supply and demand of insurance product for damaged building due to floods, it is included: age, economic circumstances, family situations, insurance motivations, and lifestyle. Simultaneously that the factors affecting supply and demand of insurance product for damaged building due to floods mounted to 65.7%.