Abstract. Tuberculosis is an infectious disease which has caused a large number of mortality in Indonesia. This disease is caused by Mycrobacterium tuberculosis. Besides affecting lung, this disease also affects other organs such as lymph gland, intestine, kidneys, uterus, bone, and brain. This article discusses the epidemic of tuberculosis through employing the SEIR model. Here, the population is divided into four compartments which are susceptible, exposed, infected and recovered. The susceptible population is further grouped into two which are vaccinated group and unvaccinated group. The behavior of the epidemic is investigated through analysing the equilibrium of the model. The result shows that administering vaccine to the susceptible population contributes to the reduction of the tuberculosis epidemic rate.
Abstract. Tuberculosis (TB) is a contagious disease which can cause death. The disease is caused by Mycobacterium Tuberculosis which generally affects lungs and other organs such as lymph gland, intestine, kidneys, uterus, bone, and brain. The spread of TB occurs through the bacteria-contaminated air which is inhaled into the lungs. The symptoms of the TB patients are cough, chest pain, shortness of breath, appetite lose, weight lose, fever, cold, and fatigue. World Health Organization (WHO) reported that Indonesia placed the second in term of the most TB cases after India which has 23 % cases while China is reported to have 10 % cases in global. TB has become one of the greatest death threats in global. One way to countermeasure TB disease is by administering vaccination. However, a medication is needed when one has already infected. The medication can generally take 6 months of time which consists of two phases, inpatient and outpatient. Mathematical models to analyze the spread of TB have been widely developed. One of them is the SEIR type model. In this model the population is divided into four groups, which are suspectible (S), exposed (S), infected (I), recovered (R). In fact, a TB patient needs to undergo medication with a period of time in order to recover. This article discusses a model of TB spread with considering the term of recovery (time delay). The model is developed in SIR type where the population is divided into three groups, suspectible (S), infected (I), and recovered (R). Here, the vaccine is given to the susceptible group and the time delay is considered in the group undergoing the medication.
This article discusses the evolution of Benjamin-Bona-Mahony (BBM) wave packet's envelope. The envelope equation is derived by applying the asymptotic series up to the third order and choosing appropriate fast-to-slow variable transformations which eliminate the resonance terms that occurred. It is obtained that the envelope evolves satisfying the Nonlinear Schrodinger (NLS) equation. The evolution of NLS envelope is investigated through its exact solution, Soliton on Finite Background, which undergoes modulational instability during its propagation. The resulting wave may experience phase singularity indicated by wave splitting and merging and causing amplification on its amplitude. Some parameter values take part in triggering this phenomenon. The amplitude amplification can be analyzed by employing Maximal Temporal Amplitude (MTA) which is a quantity measuring the maximum wave elevation at each spatial position during the observation time. Wavenumber value affects the extreme position of the wave but not the amplitude amplification. Meanwhile, modulational frequency value affects both terms. Comparison of the evolution of the BBM wave packet to the previous results obtained from KdV equation gives interesting outputs regarding the extreme position and the maximum wave peaking.
This paper concerns on propagation of Benjamin Bona Mahony (BBM) wave groups. The previous results, experimental, analytical and numerical, show that nonlinear effects will deform wave groups and may lead to large waves with wave heights larger than twice the original input; the deformation may show itself as peaking and splitting. To investigate this, especially at which location the waves will achieve their maximum amplitude, and to determine the amplitude amplification factor, a concept called Maximal Temporal Amplitude (MTA) is applied. This quantity is a tool that can be used to measure the maximum amplitude of the waves over time. In this paper we will use Benjamin-Bona-Mahony (BBM) model and third order side band approximation theory to investigate the peaking and splitting phenomena of the wave groups which is initially in bichromatic signal. The bichromatic signal here is a signal that is described by superposition of two monochromatic signals with the same value in amplitude but slightly different in frequencies. We present that the waves undergo deformation in their propagation.
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