Papers by Asep K Supriatna
Mathematics
In this paper, an SIR-SI mathematical model in the form of a system of integral equations describ... more In this paper, an SIR-SI mathematical model in the form of a system of integral equations describing the transmission of dengue disease between human and mosquitoes is proposed and analyzed. Age-dependent functions are used to describe the survival of individuals in human and mosquito populations. The basic reproduction number is derived and its relationship to the equilibria is also explored. The results show that the existence of the positive endemic equilibrium is determined by a threshold number. This threshold number is also the same one that determines the global stability of the equilibrium. The threshold acts like the known basic reproduction number in the counterpart differential equations model and also follows the same rule for the critical level of intervention. Furthermore, as an application, the effect of wolbachia infection is explored, such as how this infection changes the resulting threshold and what the consequence of its presence is in the dynamics of the disease...
Journal of Physics: Conference Series
Frontiers in Applied Mathematics and Statistics
It is crucial to take into account the dynamics of the species while investigating how a species ... more It is crucial to take into account the dynamics of the species while investigating how a species may survive in an environment. A species can be classified as either semelparous or iteroparous depending on how it reproduces. In this article, we present a model, which consists of two semelparous species by considering two age classes. We specifically discuss the effects of density-dependent in the interaction between the two semelparaous species and examine the equilibria of the system in the absence and presence of harvesting in the system. Then, the local stability of the equilibria is also investigated. A modified Leslie matrix population model with the addition of density-dependent in the equation is used. The model is analyzed in the presence and absence of competition between these species. We assume that density-dependent only occurred in the first age class of both species and that harvesting only occurred in the second age class of both species. Then, we assume that competit...
THE 4TH INTERNATIONAL CONFERENCE ON NUCLEAR ENERGY TECHNOLOGIES AND SCIENCES (ICoNETS) 2021
In the ecology of animal populations, there are two types of population reproduction strategy, na... more In the ecology of animal populations, there are two types of population reproduction strategy, namely semelparous and iteroparous reproduction strategy. Semelparous population produces only once and then die, while iteroparous population does multiple reproductive cycles over the course of a lifetime as opposed to semelparous population. Studying the dynamic behavior of the semelparous population can be done using the Leslie matrix model. The Leslie matrix model is a model that describes the dynamics of growth of the female population based on the age structure. In terms of its element, the Leslie matrix is composed of the birth rate factor in the first row that is feasible to be more than or equal to zero, the survival factor in the main subdiagonal that is feasible from zero and less than one, and the other elements are set to be zero. The Leslie matrix for the semelparous population is called the Leslie semelparous matrix where there is a change in the first-row element, that is, only the last birth rate element is worth more than zero while the others are equal to zero. In this paper, we discuss the characteristic of the Leslie semelparous matrix to reveal the dynamics behavior of semelparous populations. Our results predict the important dynamics of the semelparous population, such as the appearance of cyclical population density both for total population and for each age class.
2019 International Conference on Sustainable Engineering and Creative Computing (ICSECC)
We present the stability analysis for solution of a mathematical model of technology transfer. Th... more We present the stability analysis for solution of a mathematical model of technology transfer. The model takes form in a system of differential equations. We assume that there are two competing followers with logistic growth function of technological development for all parties involved. The analysis of the model is done via dynamical system approach by emphasizing the long-term behaviour of the system. In this paper the stability analysis of the system will be investigated. A crisp initial condition for each of the followers is assumed to show that there are two stable non-trivial equilibrium points. Both of them are co-existence equilibrium solutions, which indicates a plausible model. Some numerical examples are presented to illustrated properties of the model.
Symmetry, 2022
The primary purpose of this study is to solve the economic growth acceleration model with memory ... more The primary purpose of this study is to solve the economic growth acceleration model with memory effects for the quadratic cost function (Riccati fractional differential equation), using Combined Theorem of Adomian Polynomial Decomposition and Kashuri–Fundo Transformation methods. The economic growth model (EGM) with memory effects for the quadratic cost function is analysed by modifying the linear fractional differential equation. The study’s significant contribution is to develop a linear cost function in the EGM for a quadratic non-linear cost function and determine the specific conditions of the Riccati fractional differential equation (RFDEs) in the EGM with memory effects. The study results showed that RFDEs in the EGM involving the memory effect have a solution and singularity. Additionally, this study presents a comparison of exact solutions using Lie symmetry, Combined Theorem of Adomian Polynomial Decomposition, and Kashuri–Fundo Transformation methods. The results showed ...
Copyright © 2015 Jafaruddin et al. This is an open access article distributed under the Creative ... more Copyright © 2015 Jafaruddin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Estimating the basic reproductive ratioR 0 of dengue fever has continued to be an ever-increasing challenge among epidemiologists. In this paperwe propose two different constructions to estimateR 0 which is derived fromadynamical systemof host-vector dengue transmissionmodel.The construction is based on the original assumption that in the early states of an epidemic the infected human compartment increases exponentially at the same rate as the infectedmosquito compartment (previous work). In the first proposed construction, we modify previous works by assuming that the rates of infection for mosquito and human compartments might be different. In the second construction, we add an improvement by including more realistic conditions in whic...
SYMPOSIUM ON BIOMATHEMATICS 2019 (SYMOMATH 2019), 2020
In this paper, we propose a mathematical model of forest resources depletion caused by human expl... more In this paper, we propose a mathematical model of forest resources depletion caused by human exploitation. The human population is comprising of two subpopulations, i.e. nonindigenous people who exploit the forest unwisely (N 1) and indigenous people who exploit the forest wisely by considering nondestructive ulitization (N 2). The unwise exploitation of the forest resulting in population pressure for the forest. We assume that part of the forest (B 1) is managed by the nonindigenous people, while the remaining part (B 2) is managed by the indigenous people. It is assumed that the cumulative density of forest resources for each subpopulations and the density of human populations (both indigenous and nonindigenous populations) follow logistic models with predator-prey type nonlinear interaction terms. It is considered that the carrying capacity of forest resources decreases by population pressure. In this paper, we are looking for the effect of different management, especially the population pressure, into the forest dynamics (biomass abundance). A conservation model is also proposed to control the population pressure by providing some economic incentives to people, the amount of which is assumed to be proportional to the population pressure. The model is analyzed by using standard theory of dynamical system and numerical simulation.
In this paper we will present a mathematical model for word of mouth marketing strategy by consid... more In this paper we will present a mathematical model for word of mouth marketing strategy by considering proportional recruitment. We divide a population under consideration into four subpopulations: susceptible – those who are the target market or potential buyers ( S ), infected – those who are already active as buyers ( I ), positive – former buyers which have positive comments on the item they purchased ( P ) and negative – former buyers which have negative comments on the item they purchased ( N ). We assume that the rate of new individuals who enter the target market is proportional to the number of S , I , P , and N subpopulations. These subpopulations have either a positive or negative contribution to the number of new entry to the susceptible class or the potential buyer. We analyzed the model emphasizing in the effects of the WOM on the number of buyers and its rate of increase.
Maximum Sustainable Yield (MSY) is an important concept in fisheries management. It represents th... more Maximum Sustainable Yield (MSY) is an important concept in fisheries management. It represents the maximum amount of biomass that are allowed to be taken as a harvest without harming the sustainability of the fisheries. The value of the MSY is a function of the growth parameters of the harvested population. Since the MSY is not stable, knowing the right growth parameters of the population is critical in determining the MSY. Using an inaccurate values of growth parameters is likely detrimental in applying the MSY to the real fisheries. Hence, to reduce the error in calculating these growth parameters we need a good tool or software. In this paper we present a software as a Decision Support System (DSS) to estimate the values of the growth parameters from the yield effort data of a harvested population and to suggest the value of the maximum sustainable yield as a decision to the harvester in managing the population. The software is developed using C# programming language in windows f...
Decision Science Letters, 2022
The power-law memory effect is taken into consideration in a generalisation of the economic model... more The power-law memory effect is taken into consideration in a generalisation of the economic model of natural growth. The memory effect refers to a process's reliance on its current state and its history of previous changes. However, the study that focuses on natural growth in economics considering the memory effect with fractional order-linear differential equation model is still limited. The current investigation seeks to solve the natural growth with memory effect in the economics model and decide the best model using fractional differential equation (FDE), namely Adomian Decomposition and Variational Iteration Methods. Also, this study assumes the level of consumer loss memory during a certain time interval denoted by a parameter (α). This study showed the model of loss memory effect with 0 < α ≤ 1 given a slowdown in output growth compared to a model without memory effect. Besides that, this study also found that output Y(t) is growing faster with the Variational Iteratio...
2017 4th International Conference on Control, Decision and Information Technologies (CoDIT), 2017
In this paper, we study a two-dimensional maintenance contract for a fleet of trucks such as dump... more In this paper, we study a two-dimensional maintenance contract for a fleet of trucks such as dump truck operated in a mining industry. The trucks are sold with a two-dimensional warranty. The warranty and the maintenance contract are characterized by two parameters (i.e. age and usage limits) which define a 2-dimensional region. The maintenance service contracts studied is the one which offers policy limit cost to protect a service provider (an agent) from over claim and to pursue the owner to do maintenance under specified cost inhouse. This in turn gives benefit for both the owner of the trucks and the agent of service contract. The decision problem for an agent is to determine the optimal price for each options offered and for the owner is to select the best contract option. We use a Nash game theory formulation in order to obtain a win-win solution — i.e. the optimal price for the agent and the optimal option for the owner.
International Journal of Artificial Intelligence & Applications, 2021
Facial expression recognition is one of the types of non-verbal communication that is not only co... more Facial expression recognition is one of the types of non-verbal communication that is not only commons for human but also plays an essential role in everyday lives. The development of science and technology allows the machine to automatically detect human facial expressions based on images and videos. Numerous facial expression detection methods have been proposed in the literature. This paper presents a method to find three basic facial expressions (neutral, happy, and angry) from two parameter values: smile and eyes-open. The analysis involves a preprocessing step using a combination of pre-designed proprietary algorithm and Luxand library. Firstly, the parameters were mapped into two-dimensional space and then grouped into three clusters using K-means, a popular heuristic clustering method. Secondly, more than 50,000 frames for each video were experimented using the proprietary research data. The result shows that the proposed method successfully performed a simple video analysis...
Journal of Physics: Conference Series, 2021
Twitter is a social network that is very popular among the people that allows the users to send a... more Twitter is a social network that is very popular among the people that allows the users to send and read text-based messages up to 140 characters, known as tweets. Since it was first launched until now, this social network has become one of the ten most visited sites on the internet. Because there are so many people use this social network, Twitter has become a source of information that can disseminate information in a short time. Dissemination of information on Twitter is very preferred by the accounts of Twitter users. The most important account in the dissemination of information on Twitter can be searched by calculating the centrality measurement. In this paper, four centrality measures are used to find the most important accounts, that are degree centrality, closeness centrality, betweenness centrality, and eigenvector centrality. Before calculating the centrality of the Twitter accounts, data must be collected first, wherein this paper the data to be used is tweeted data from...
IOP Conference Series: Materials Science and Engineering, 2018
In this paper, we discuss a mathematical model of plant disease with the effect of fungicide. We ... more In this paper, we discuss a mathematical model of plant disease with the effect of fungicide. We assume that the fungicide is given as a preventive treatment to infectious plants. The model is constructed based on the development of the disease in which the monomolecular is monocyclic. We show the value of the Basic Reproduction Number (BRN) ℛ of the plant disease transmission. The BRN is computed from the largest eigenvalue of the next generation matrix of the model. The result shows that in the region where ℛ greater than one there is a single stable endemic equilibrium. However, in the region where ℛ less than one this endemic equilibrium becomes unstable. The dynamics of the model is highly sensitive to changes in contact rate and infectious period. We also discuss the optimal control of the infected plant host by considering a preventive treatment aimed at reducing the infected host plant. The obtaining optimal control shows that it can reduce the number of infected hosts compared to that without control. Some numerical simulations are also given to illustrate our analytical results.
IOP Conference Series: Materials Science and Engineering, 2018
In this paper we develop a mathematics model of population growth in the West Java Province Indon... more In this paper we develop a mathematics model of population growth in the West Java Province Indonesia. The model takes the form as a logistic differential equation. We parameterize the model using several triples of data, and choose the best triple which has the smallest Mean Absolute Percentage Error (MAPE). The resulting model is able to predict the historical data with a high accuracy and it also able to predict the future of population number. Predicting the future population is among the important factors that affect the consideration is preparing a good management for the population. Several experiment are done to look at the effect of impreciseness in the data. This is done by considering a fuzzy initial value to the crisp model assuming that the model propagates the fuzziness of the independent variable to the dependent variable. We assume here a triangle fuzzy number representing the impreciseness in the data. We found that the fuzziness may disappear in the long-term. Other scenarios also investigated, such as the effect of fuzzy parameters to the crisp initial value of the population. The solution of the model is obtained numerically using the fourth-order Runge-Kutta scheme.
IOP Conference Series: Materials Science and Engineering, 2018
Tourism sector has a tendency to be proposed as a support for national economy to many countries ... more Tourism sector has a tendency to be proposed as a support for national economy to many countries with various of natural resources, such as Indonesia. The number of tourist is very related with the success rate of a tourist attraction, since it is also related with planning and strategy. Hence, it is important to predict the climate of tourism in Indonesia, especially the number of domestic or international tourist in the future. This study uses Seasonal Autoregressive Integrated Moving Average (SARIMA) time series method to predict the number of tourist arrival to tourism strategic areas in Nusa Tenggara Barat. The prediction was done using the international and domestic tourist arrival to Nusa Tenggara Barat data from January 2008 to June 2016. The established SARIMA method was ሺ0,1,1ሻሺ0,0,2ሻ ଵଶ with MAPE error of 15.76. The prediction for the next six time periods showed that the highest number of tourist arrival is during September 2016 with 330,516 tourist arrivals. Prediction of tourist arrival hopefully might be used as reference for local and national government to make policies to strengthen national economy for a long period of time
Jurnal Teknologi, 2016
This paper discusses a matrix model that describes the dynamics of a population with m live stage... more This paper discusses a matrix model that describes the dynamics of a population with m live stages and lives in n patch seen from algebra viewpoint. The matrix D describes population growth in a patch or location. The matrix D is defined as a matrix obtained from matrix multiplication of a permutation matrix with a block diagonal matrix that its diagonal blocks is matrices with non-negative entries and transpose of a permutation matrix [4]. It will be shown that the permutation matrix contained in D has a special form.
IOP Conference Series: Materials Science and Engineering, 2019
Indonesia has a remarkable potential in tourism sector, hence government should regulate all matt... more Indonesia has a remarkable potential in tourism sector, hence government should regulate all matters related with tourism and pay more attention to the developments happening in the tourism sector, including policy-making and planning. One way to aid the government in policy making and planning is by conducting a prediction about the number of incoming international tourists to Indonesia. This paper will elaborate the analysis about the comparison between multiplicative Holt-Winter and decomposition method in predicting the number of incoming international tourists to Indonesia. This paper aims to determine the appropriate forecasting method suitable for the available data pattern and provides more accurate forecasting result. Forecasting could be conducted using multiplicative Holt-Winter method and decomposition method. Meanwhile to determine the error level and forecast accuracy, mean absolute percentage error (MAPE) is used. Analysis result showed that prediction using Holt-Winter method provides MAPE of 4.7098%, meanwhile the MAPE for decomposition method is 3.3254%. It could be concluded that to determine the number of incoming international tourist to Indonesia, decomposition method is more appropriate.
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Papers by Asep K Supriatna