Dinamika kebiasaan merokok dalam artikel ini dianalisis dengan pendekatan model epidemiologi. Lingkungan perokok dibagi menjadi empat populasi, yaitu populasi (Potential) menyatakan populasi dari ...individu-individu yang tidak merokok, populasi (Light) menyatakan populasi dari perokok ringan, populasi (Smokers) menyatakan populasi dari perokok berat, populasi menyatakan populasi dari individu-individu yang berhenti merokok sementara dan populasi menyatakan populasi dari individu-individu yang berhenti merokok secara permanen. Model tersebut dimodifikasi kemudian dianalisis titik ekuilibriumnya. Langkah pertama, ditentukan titik ekuilibrium bebas rokok. Langkah kedua, ditentukan titik ekuilibrium kebiasaan merokok. Langkah ketiga, ditentukan the Smoking Generation Number (R0 ) dengan menggunakan next generation matrix yang melibatkan radius spektral. Langkah terakhir, kestabilan lokal setiap titik ekuilibrium pada modelnya dianalisis. Hasil analisis menunjukkan bahwa titik ekuilibrium bebas rokok stabil asimtotik lokal saat nilai the Smoking Generation Number kurang dari satu. Sebaliknya, jika nilai the Smoking Generation Number lebih dari satu dan b1(m+g) lebih dari b2(b1-m), maka titik ekuilibrium perokok ringan stabil asimtotik lokal. Sedangkan titik ekuilibrium perokok berat stabil asimtotik lokal jika nilai the Heavy Smoking Generation Number lebih dari satu. Kemudian dilakukan simulasi numerik menggunakan Software Maple untuk mengecek hasil analisis kestabilan lokal titik ekuilibrium tersebut.
The SIR-SI mathematical model for the problem of dengue virus spread which has been discussed in previous studies has not involved the saturated birth rate of mosquito. This discussion aims to ...construct and analyze the SIR-SI model which involves competition factors in mosquito population growth so that the model used to predict the number of dengue virus infections becomes more realistic. In addition, sensitivity analysis and numerical simulations of the models that have been constructed are also discussed. The method used is a literature study using theories derived from reputable articles. The results of this discussion show that the existence of an equilibrium point and its stability depends on the basic reproduction number. If the basic reproduction number is less than one, the number of cases of dengue fever infection will decrease. However, if the basic reproduction number is more than one, the number of cases of dengue infection will not decrease and even tend to be constant at a certain number. The average parameter of bites carried out by one mosquito in all humans () is the most dominant in increasing the spread of dengue disease in humans. On the other hand, mosquitoes' natural death rate parameter () is the most dominant in reducing the spread of dengue fever in humans. This information provides input and evaluation to decision-makers in solving the problem of the spread of dengue fever.
A crucial part of illness prevention over the past few decades has been played by mathematical models. The dynamic system can be used to characterize the TB infection process. For the purpose of ...developing future prevention strategies, it is crucial to comprehend the effect of vaccination approach on the control of TB. We investigated the impact of vaccination strategies on TB disease transmission through a dynamic model. The model discussed involves logistical population growth. The purpose of this discussion is to analyze the local stability of the equilibrium point of the TB disease transmission model. Numerical simulations are provided to illustrate the theoretical results. The existence and local stability of the model equilibrium point depends on the basic reproduction number analytically. Based on secondary data, the basic reproduction number values are 0.98 and 4.12, respectively. Numerical simulations for these two values support the analysis results obtained. If the basic reproduction number is less than one, then the transmission of TB disease can be eradicated. However, if the basic reproduction number is more than one, the vaccination strategy is not sufficient to control TB transmission.
This study is expected to contribute to the health sector, specifically to describe the dynamics of the measles spread through the models that have been analyzed. One of the factors that became the ...focus of this study was reviewing the influence of population density on measles spread. The initial step formulated the model and then determined the primary reproduction number and analyzed the stability of the model equilibrium point. The results of the analysis of this model show that there are two conditions for the value of which is a requirement that the existence of two model equilibrium points as well as local stability is needed, namely and . When , there exists a unique equilibrium point, called the non-endemic equilibrium point denoted by . Conversely, when , there are two equilibrium points, namely and the endemic equilibrium point characterized by . The results of local stability analysis show that when , the equilibrium point is stable asymptotic locally. It means that if hold, then in a long time there will not be a spread of disease in the susceptible and vaccinated sub-population, or in other words, the outbreak of the disease will stop. Conversely, when equilibrium point is stable asymptotic locally. It means that if , then measles disease is still in the environment for an infinite time with the condition of the proportions of each sub-population approach to , , and .
Abstrak
Artikel ini termasuk dalam ruang lingkup matematika epidemiologi. Tujuan ditulisnya artikel ini untuk mendeskripsikan dinamika lokal penyebaran suatu penyakit dengan beberapa asumsi yang ...diberikan. Dalam pembahasan, dianalisis titik ekuilibrium model epidemi SVIR dengan adanya imigrasi pada kompartemen vaksinasi. Dengan langkah pertama, model SVIR diformulasikan, kemudian titik ekuilibriumnya ditentukan, selanjutnya, bilangan reproduksi dasar ditentukan. Pada akhirnya, kestabilan titik ekuilibirum yang bergantung pada bilangan reproduksi dasar ditentukan secara eksplisit. Hasilnya adalah jika bilangan reproduksi dasar kurang dari satu maka terdapat satu titik ekuilbirum dan titik ekuilbrium tersebut stabil asimtotik lokal. Hal ini berarti bahwa dalam kondisi tersebut penyakit akan cenderung menghilang dalam populasi. Sebaliknya, jika bilangan reproduksi dasar lebih dari satu, maka terdapat dua titik ekuilibrium. Dalam kondisi ini, titik ekuilibrium endemik stabil asimtotik lokal dan titik ekuilibrium bebas penyakit tidak stabil. Hal ini berarti bahwa dalam kondisi tersebut penyakit akan tetap ada dalam populasi.
Kata Kunci : Model SVIR, Stabil Asimtotik Lokal
Abstract
This article is included in the scope of mathematical epidemiology. The purpose of this article is to describe the dynamics of the spread of disease with some assumptions given. In this paper, we present an epidemic SVIR model with the presence of immigration in the vaccine compartment. First, we formulate the SVIR model, then the equilibrium point is determined, furthermore, the basic reproduction number is determined. In the end, the stability of the equilibrium point is determined depending on the number of basic reproduction. The result is that if the basic reproduction number is less than one then there is a unique equilibrium point and the equilibrium point is locally asymptotically stable. This means that in those conditions the disease will tend to disappear in the population. Conversely, if the basic reproduction number is more than one, then there are two equilibrium points. The endemic equilibrium point is locally asymptotically stable and the disease-free equilibrium point is unstable. This means that in those conditions the disease will remain in the population.
Keywords: SVIR Model, Locally Asymptotically stable.
The Commission for the Supervision of Business Competition, known as the KPPU, ruled that a consortium made up of state-owned gas and oil company PT Pertamina, listed gas and oil producer PT Medco ...Energi and its PT Medco E&P Tomori Sulawesi unit colluded with Mitsubishi to help the Japanese company win a contract to build a gas storage facility at the $1.8 billion Donggi-Senoro liquefied-natural-gas plant in central Sulawesi.
Tea plantation biomass wastes, such as tea plantation pruning, shade trees, and woody weeds have not been utilized. The waste can be used as renewable energy in the form of wood pellets. The problem ...is the feasibility of biomass waste to be used as material for making wood pellets as energy. This paper aims to analyze the potential of tea plantation biomass waste as wood pellet material to meet energy needs. The research was conducted in a tea plantation owned by the Tea and Kina Research Center (PPTK). Quantification of biomass waste potential per unit area was conducted in the plantation using direct measurement method. Proximate analysis of each wood pellet variant of biomass waste was conducted to match the quality of Indonesian Wood Pellet Standard. The biomass waste potential in PPTK is 14,281 tons per year which can produce 8,186 tons of wood pellets per year. This potential can meet the needs of wood pellet consumption from the tea production process at PPTK which is around 1.8 tons / day for the tea processing process of 13 tons/day. Based on proximate analysis, the wood pellets produced have a calorific value of 4425 cal/gram, density of 1.35 grams/cm3, fixed carbon content of 85.2%, and volatile matter of 3.72%. These results confirm that the wood pellets comply with the National Wood Pellet Standard (SNI 8021:2014). This can be a model for the application of the Green Circular Economy concept in the plantation sector. Keywords: Biomass pellets; Green circular economy; Renewable energy; Tea plantation waste; Wood pellets
Introduction: Being treated in isolation rooms for people infected with COVID-19, creates various perceptions of uncertainty, especially when strict "health protocols" are applied. This study aims to ...determine the understanding patients with COVID in the intensive care unit from the perspective of care. Materials and Methods: The research design used phenomenological qualitative with in-depth interviews. Purposive sampling was used with interpretive phenomenological analysis. Participants were 25 patients who had been exposed to COVID-19, consisting of 10 men and 15 women. Results: This study resulted in the theme of the perception of COVID-19 sufferers while undergoing treatment in isolation rooms, with four themes, namely, 1) mental attacks, 2) feel like fighting alone, 3) expecting Concern, 4) positive attitude. Conclusion: This analysis shows that various perceptions of uncertainty that are felt while being treated in the isolation room due to suffering from COVID-19 disease can be anticipated by increasing the awareness of nurses to be closer to patients through caring-based nursing practices by emphasizing meaningful interpersonal relationships. Keywords: perception, COVID-19, nursing, isolation room, caring
One important innovation of green construction material is natural polymer modified mortar. In this research, polymer modified mortar used natural polymer from seaweeds, they are Eucheuma Cottonii ...(gel) and Gracilaria Sp. The research conducted in two parts, pre-experiment and main-experiment. Pre-experiment aimed to investigate compressive strength of natural polymer modified mortar with seaweed gel (Eucheuma Cottonii) and seaweed powder (Gracilaria Sp.). The pre-experiment followed by main-experiment which investigated compressive strength and splitting tensile strength. The research has shown that natural polymer modified mortar with seaweed powder (Gracilaria Sp.) performed great compressive strength and splitting tensile with optimum mix composition of KM-0.5.
A 25.5 km long access road has been constructed in a hilly area in Cisokan region. Several slope instabilities occurred during the rainy season, particularly at the end of heavy rainfall. A ...comprehensive study was performed to understand the characteristics of rainfall-induced slope instability. The study consisted of field observation, analyses of field and laboratory test data, and numerical analyses. The study revealed that in general there were two categories of slopes with instability characteristics: (i) slopes with a significant groundwater level increase during rainfall; (ii) slopes with an insignificant groundwater level increase during rainfall. In the first category, the slope instability was caused by a loss of matric suction and eventually the pore-water pressure, uw became positive as indicated by an increase of the groundwater level. In the second category, the slope instability was caused by a loss of matric suction without a rise in pore-water pressure, uw, to a positive magnitude. Two empirical curves of slope stability were developed as a preliminary guidance to assess slope stability during rainfall in the region.
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