Mathematical Model as a Tool for the Control of Vector-Borne Diseases: Wolbachia Example

Dengue is a vector-borne disease that risks two-thirds of the world’s population particularly in tropical and subtropical regions. Strategies have been implemented, but they are only effective in the short term. A new innovative and promising strategy against dengue is by the use of Wolbachia bacterium. This requires that Wolbachia-carrying mosquitoes should persist in the population. To assess the persistence of Wolbachia-carrying mosquitoes and its effects on dengue, a number of mathematical models have been formulated and analysed. In this chapter, we review the existing mathematical models of Wolbachia-carrying mosquito population dynamics and dengue with Wolbachia intervention and provide examples of the mathematical models. Simulations of the models are presented to illustrate the model’s solutions

Pengembangan Modul Elektronik Matematika pada Bahasan Eksponensial dan Logaritma Menggunakan Pendekatan Saintifik

Tujuan dari penelitian ini adalah mengembangkan modul elektronik matematika pada pokok bahasan eksponensial dan logaritma dengan menggunakan pendekatan saintifik pada kelas X SMA. Metode penelitian ini merupakan penelitian dan pengembangan (research and development) dan menggunakan model pengembangan Borg and Gall yang melibatkan lima Langkah, yaitu (1) melakukan analisis produk yang akan dikembangkan, (2) mengembangkan produk awal, (3) validasi ahli dan revisi, (4) uji coba lapangan skala kecil dan revisi produk, dan (5) uji coba lapangan skala besar dan produk akhir. Penelitian dilakukan pada Desember 2020 di SMA IT Al-Halimiyah. Berdasarkan hasil validasi modul elektronik matematika oleh ahli materi dan bahasa diperoleh persentase secara keseluruhan aspek sebesar 84,19% serta validasi ahli media 81,30%. Kemudian, menurut hasil evaluasi guru diperoleh persentase keseluruhan aspek sebesar 89,57%. Pada uji coba lapangan skala kecil diperoleh hasil 94,90% untuk persentase secara keseluruhan. Serta ketika uji coba lapangan skala besar diperoleh persentase sebesar 88,31%

Stability analysis rabies model in animals with the effect of vaccination and sterilization

A deterministic model for the transmission dynamics of the rabies virus in animals is formulated. The effect of rabies vaccine, surgical sterilization and rabies immuno-contraceptive vaccine is considered in the model, then the stability of the disease-free equlilibrium is analyzed to get the basic reproduction number using the next generation matrix method. Both local stability and global stability of the model are analyzed and written down as theorems