The effect of word-of-mouth marketing strategy on the number of buyers: a mathematical perspective

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

Model Matematika Penyebaran Penyakit Demam Berdarah

Di dalam paper ini dibahas model matematika deterministik untuk penyebaranpenyakit demam berdarah. Ambang batas epidemik dapat ditentukan sebagaifungsi dari pertumbuhan nyamuk Aedes aegypti. Pertumbuhan nyamuk ini jugamenentukan kestabilan dari state bebas demam berdarah dan state endemikdemam berdarah. Analisis selanjutnya memperlihatkan bahwa pengontrolanepidemik yang efektif adalah dengan cara mengontrol pertumbuhan nyamuktersebut secara periodik

Alternative Branching Strategies in the Branch and Bound Algorithm by Using a k-clique covering vertex set for Maximum Clique Problems.

The Maximum clique problem (MCP) is graph theory problem that demand complete subgraf with maximum cardinality (maximum clique) in arbitrary graph. Solving MCP usually use Branch and Bound (BnB) algorithm, in this paper we will show how n + 1 color classes (where n is the difference between upper and lower bound) selected to form k-clique covering vertex set which later used for branching strategy can guarenteed finnding maximum clique

The dynamics of prisoner population model in Indonesia with a rehabilitation regulation for drug users to overcome prison overcapacity issue

This paper discusses about a mathematical model of the prisoner population with a new regulation regarding punishments to the drug users in an effort to overcome the prison overcapacity issue in Indonesia. This new regulation is launched by the Indonesia government after a fact about overcapacity of prison in Indonesia is revealed through a fire incident in a prison on 8 September 2021 that causes 41 people died and a number of people were injured. Besides, prisons in Indonesia are mostly occupied by the drug user. The model is constructed by using a compartmental model approach. The stability analysis of the equilibrium points is carried out along with its existence conditions. The analytical studies are equipped by calculate the basic reproduction number. Furthermore, this study is also equipped by numerical simulations with some scenarios. The results of this study confirm that the effect of the new regulation is able to reduce overcrowded issue in prisons in Indonesia. However, if it compare to recent prison capacity, this new regulation has not been able to suppress the number of prisoner below to its capacity limit in the short time so that it is needed to consider other solutions as the additional regulation and polic

Comparison of the differential transformation method and non standard finite difference scheme for solving plant disease mathematical model

The Differential Transformation Method (DTM) and the Non Standard Finite Difference Scheme (NSFDS) are alternative numerical techniques used to solve a system of linear and nonlinear differential equations. In this paper, we construct the DTM and NSFDS for a mathematical model of plant disease transmission dynamics and compare their solutions to that generated by MATLAB ode45 routine, which is the well-established numerical routine. The solutions of the DTM and NSFDS are in good agreement with MATLAB ode45 routine in the small time step. However, when the time step is larger, the NSFDS performs better than the DTM

ANALISIS PEREMAJAAN ANGKUTAN KOTA Studi Kasus : Angkot Trayek Margahayu Raya – Ledeng

Dalam paper ini dibahas suatu model matematika untuk peremajaan angkutan kota. Model yang dibentuk berupa model yang kontinu. Model kemudian diaplikasikan untuk menentukan umur ekonomis angkutan kota trayek Margahayu Raya – Ledeng di Bandung, dalam kaitannya dengan peremajaan angkutan kota yang bersangkutan. Lebih jauh lagi umur ekonomis yang diperoleh ini kemudian dibandingkan dengan berbagai skenario, seperti tingkat suku bunga yang berbeda, tingkat utilitas yang berbeda dan harga bahan bakar minyak yang berbeda. Kata kunci : Umur Ekonomis, Peremajaan Angkutan Kot

KONTROL OPTIMAL VAKSINASI MODEL EPIDEMIOLOGI TIPE SIR

Paper ini mengkaji kontrol optimal vaksinasi dari model epidemiologi tipe SIR dengan adanya reinfeksi, dimana S adalah individu kompartemen susceptible, I adalah individu kompartemen infected, dan R adalah individu kompartemen recovered. Kontrol optimal vaksinasi dilakukan untuk mengetahui efektifitas vaksin pada pencegahan penyebaran suatu penyakit menular. Pada model ini juga ditentukan angka reproduksi dasar, titik ekuilibrium endemik dan nonendemik. Selanjutnya diberikan perhitungan numerik dengan menggunakan program Matlab untuk ilustrasi pengaruh kontrol vaksinasi terhadap kompartemen terinfeksi. Kata kunci: Kontrol optimal, vaksinasi, tipe SIR, titik ekuilibrium, angka reproduksi dasar

MODEL MATEMATIKA PENYEBARAN PENYAKIT DEMAM BERDARAH

Di dalam paper ini dibahas model matematika deterministik untuk penyebaranpenyakit demam berdarah. Ambang batas epidemik dapat ditentukan sebagaifungsi dari pertumbuhan nyamuk Aedes aegypti. Pertumbuhan nyamuk ini jugamenentukan kestabilan dari state bebas demam berdarah dan state endemikdemam berdarah. Analisis selanjutnya memperlihatkan bahwa pengontrolanepidemik yang efektif adalah dengan cara mengontrol pertumbuhan nyamuktersebut secara periodik.Kata kunci : model matematika, demam berdarah, ambang batas epidemik, state bebas demamberdarah, state endemik demam berdarah, kestabilan titik tetap, Aedes aegypt

An Analysis of Covid-19 Transmission in Indonesia and Saudi Arabia

An outbreak of novel coronavirus has been happening in more than 200 countries and has shocked society. Several measures have been implemented to slowing down the epidemics while waiting for vaccine and pharmaceutical intervention. Using a deterministic and stochastic model, we assess the effectiveness of current strategies: reducing the transmission rate and speeding up the time to detect infected individuals. The reproductive ratio and the probability of extinction are determined. We found that the combination of both strategies is effective to slow down the epidemics. We also find that speeding up the time to detect infected individuals without reducing the transmission rate is not sufficient to slow down the epidemics