A Game Dynamic Modeling Framework to Understand the Influence of Human Choice to Vaccinate or to Reduce Contact with Mosquitoes on Dengue Transmission Dynamics

Strategies for reducing dengue incidence are by minimizing the contact between mosquitoes and human or the use of vaccine. However, the candidate of dengue is not perfect and potentially results in more secondary infection cases.This leads to the question which strategy should be decided by individuals to reduce the chance for being infected by dengue. A game-dynamic modeling framework by coupling epidemic and behavior model has been constructed to study the effects of human decision making behavior on dengue transmission dynamics. We also consider strategies as time-dependent controls and estimate the parameter values against data of dengue incidence in Kupang city, Indonesia. Parameter estimation gives the reproduction number of 1.17 which indicates the possibility of outbreak occurrence. When the efficacy of reduced contact with mosquitoes is low, the use of vaccination is the best option to reduce dengue incidence. The efficacy of reduced contact with mosquitoes should be at high level to get higher reduction in dengue incidence if no vaccine is available yet. An optimal control approach suggests that a higher level of vaccination rate and the reduced contact with mosquitoes is required to reach optimal reduction in dengue incidence. However, solutions from epidemiological-behavior model showed that individuals are likely to choose one strategy only which has higher cost and the probability of perceived efficacy. The implementation of vaccination helps in reducing dengue incidence. However, understanding the effects of dengue vaccine on secondary infections is required before the delivery of such intervention

APPLICATION OF DIFFERENTIAL TRANSFORMATION METHOD FOR SOLVING HIV MODEL WITH ANTI-VIRAL TREATMENT

Mathematical models have been widely used to understand complex phenomena. Generally, the model is in the form of system of differential equations. However, when the model becomes complex, analytical solutions are not easily used and hence a numerical approach has been used. A number of numerical schemes such as Euler, Runge-Kutta, and Finite Difference Scheme are generally used. There are also alternative numerical methods that can be used to solve system of differential equations such as the nonstandard finite difference scheme (NSFDS), the Adomian decomposition method (ADM), Variation iteration method (VIM), and the differential transformation method (DTM). In this paper, we apply the differential transformation method (DTM)  to solve system of differential equations. The DTM is semi-analytical numerical technique to solve the system of differential equations and provides an iterative procedure to obtain the power series of the solution in terms of initial value parameters. In this paper, we present a mathematical model of HIV with antiviral treatment and construct a numerical scheme based on the differential transformation method (DTM) for solving the model. The results are compared to that of Runge-Kutta method. We find a good agreement of the DTM and the Runge-Kutta method for smaller time step but it fails in the large time ste

Modeling and Prediction of COVID-19 with a Large Scale Social Distancing

Coronavirus 2019 (COVID-19), yang kasusnya dimulai di Cina, dalam kurun waktu dua bulan telah menyebar dengan cepat ke lebih dari 114 negara dan territorial. Pemahaman tentang dinamika penularan Covid-19 sangat penting untuk menentukan kebijakan dan strategi dalam pengobatan dan pengendalian penyebaran penyakit ini. Dalam makalah ini, disusun model matematika yang menggambarkan dinamika penularan penyakit menggunakan model matematika deterministik dengan menggunakan data penyebaran COVID-19 di Jakarta, Indonesia dari 3 Maret 2020, hingga 10 April 2020. Model berbentuk Sistem persamaan diferensial yang selanjutnya dilakukan analisis matematika dan simulasi numerik. Hasil simulasi menunjukkan bahwa tanpa intervensi, angka reproduksi penyebaran Covid-19 di Provisi Jakarta sekitar 1,658 dan jika Pembatasan Sosial Berskala Besar (PSBB) diimplementasikan, maka angka reproduksinya turun menjadi 1,40. Lebih lanjut, epidemi diperkirakan akan berakhir sekitar akhir November 2020 dengan kasus puncak pada pertengahan Juni 2020 dengan jumlah orang yang dikonfirmasi positif terinfeksi mencapai sekitar 9.000 jiwa. Dari hasil pemodelan ini, disimpulkan bahwa untuk meminimalkan penularan penyakit, perlu menerapkan kebijakan dan kontrol yang lebih ketat. [Coronavirus disease 2019 (COVID-19) which was initiated in China, has spread rapidly in more than 114 countries and territories over the last two months. An understanding of the dynamics of Covid-19 transmission is very important to determine policies and strategies in the treatment and control of the spread of this disease. In this paper, we formulated a mathematical model that describes the transmission dynamics of the disease using a deterministic mathematical model and the model is validated against data from Jakarta, Indonesia from March 3, 2020, to April 10, 2020. Mathematical analysis and numerical simulations are presented. We found that without intervention, the reproduction number is around 1.658 and the reproduction number declines to 1.40 if large scale social distancing is implemented. Furthermore, the end time of epidemic is predicted to be around the end of November 2020 with peak cases around mid-June 2020 and the number of confirmed infected individuals is around 9,000. To minimize the transmission of the diseases, it is necessary to enforce strict policies and controls.

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

DETERMINISTIC AND STOCHASTIC DENGUE EPIDEMIC MODEL: EXPLORING THE PROBABILITY OF EXTINCTION

Dengue, a vector-borne disease, threatens the life of humans in tropical and subtropical regions. Hence, the dengue transmission dynamics need to be studied. An important aspect to be investigated is the probability of extinction. In this paper, deterministic and stochastic dengue epidemic models with two-age classes have been developed and analyzed, and the probability of extinction has been determined.  For the stochastic approach, we use the Continuous-Time Markov Chain model. The results show that vaccination of adult individuals leads to a lower number of adult infected individuals. Furthermore, the results showed that a higher number of initial infections causes a low probability of dengue extinction. Furthermore, factors contributing to an increase in the infection-related parameters have to be minimized to increase the potential reduction of dengue cases

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

ANALISIS KARAKTER DOSEN DALAM MELAKUKAN PENELITIAN DENGAN METODE CHI-SQUARE AUTOMATIC INTERACTION DETECTION (CHAID)

Penelitian merupakan bagian dari Tri Dharma perguruan tinggi dan menjadi salah satu tugas seorang dosen serta menjadi alat ukur kinerja seorang dosen dalam menjalankan tanggung jawabnya. Tujuan penelitian ini adalah untuk mengetahui ada tidaknya pengaruh faktor umur, jenis kelamin, jabatan fungsional akademik, masa kerja, jenjang pendidikan, status pernikahan, jumlah tanggungan, dan beban mengajar terhadap produktivitas dosen dalam mengusul proposal penelitian hibah sumber dana Ristekdikti, serta menjelaskan hubungan/asosiasi berstruktur antar faktor yang mempengaruhi pengelompokan pengamatan menurut variabel terikat (produktivitas dosen dalam mengusul proposal penelitian hibah sumber dana Ristekdikti). Metode analisis yang digunakan adalah metode CHAID (Chi-square Automatic Interaction Detection) yaitu metode yang digunakan untuk menganalisis keterkaitan struktural antara peubah dalam segugus data. Hasil CHAID adalah pohon keputusan atau dendogram yang membentuk hubungan berstruktur antar variabel. Hasil dendogram CHAID menunjukkan bahwa variabel yang mempengaruhi pengklasifikasian produktivitas dosen dalam pengusulan proposal adalah jabatan fungsional, status pernikahan, dan tingkat pendidikan. Klasifikasi/pemisahan pertama didasari oleh peubah jabatan fungsional dosen. Pada tahap pertama pemisahan CHAID, peubah yang mempunyai asosiasi paling nyata dalam menentukan produktivitas dosen dalam mengusul proposal adalah jabatan fungsional yang terbagi atas dua node/cabang yaitu kelompok 1 (Lektor, Lektor kepala dan Guru besar) dan kelompok 2 (asisten ahli). Dosen yang mengusul proposal penelitian hibah sumber dana Ristekdikti terdiri atas dua kelompok. Pertama, yaitu dosen yang memiliki jabatan fungsional minimal lektor, sudah menikah, dan berpendidikan minimal S2, sedangkan yang kedua adalah dosen yang memiliki jabatan fungsional asisten ahli juga berpendidikan S3. Untuk dosen yang tidak mengusul proposal juga terdiri atas dua kelompok, yaitu kelompok dosen dengan fungsional minimal lektor yang belum menikah/cerai, dan kelompok dosen asisten ahli yang berpendidikan S2. Asosiasi berstruktur terjadi pada variabel jabatan fungsional, status pernikahan dan tingkat pendidikan. &nbsp