No abstract

A within-host tuberculosis model describing the interaction between macrophages and Mycobacterium tuberculosis was developed and analyzed in this paper. We derive R 0 as the threshold value of the model and analyze the existence and stability of equilibrium points. Furthermore, bifurcation analysis performed based on the use of the application of the center manifold theory. Explicit condition for the existence of backward bifurcation is given. Finally, numerical simulations are presented to support the theoretical findings.

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.]

No abstract

Acute myeloid leukemia (AML) is a malignant hematopoietic disorder characterized by uncontrolled proliferation of immature myeloid cells. In the AML cases, the phosphoinositide 3-kinases (PI3K)/AKT signaling pathways are frequently activated and strongly contribute to proliferation and survival of these cells. In this paper, a mathematical model of the PI3K/AKT signaling pathways in AML is constructed to study the dynamics of the proteins in these pathways. The model is a 5-dimensional system of the first-order ODE which describes the interaction of the proteins in AML. The interactions between those components are assumed to follow biochemical reactions, which are modelled by Hill’s equation. From the numerical simulations, there are three potential components targets in PI3K/AKT pathways to therapy in the treatment of AML patient.