الدّراسة النّقدية لكتاب “Muslim Tradition” في ضوء الكتاب البدر المنير للإمام ابن الملقّن

Dr. Juynboll (1935-2010) was an Orientalist. He was born in Leiden, South Holland and obtained his doctoral degree in 1969. He worked at the University of California. He was a specialist of Hadith. In 1983, Cambridge University Press published his work “Muslim Tradition: Studies in Chronology, Provenance and Authorship of Early Hadith”. This work contains a critical assessment of the persons who were involved in the formation of Islamic orthodoxy. Imam Ibnul Mulaqqi is a Muslim Scholar who examined Ahadith of the Holy Prophet (PBUH)‎ and did exhaustive work in pointing out ‎the reasons of hidden weakness in it. So through this article we will be able to judge the views and opinions of ‎ Dr. Juynboll about the Provenance and Authorship of Early Hadith and methodology of a Muslim Scholar for scrutinizing and examining the collection of Ahadith through his historical book “Albdrul-Muneer”‎.

Mathematical Analysis and Control Strategies of Hiv-1 Infection Models

In this research, we will present mathematical analysis and optmal control strategies to control the spread of HIV-1 infection. For this, first we will develop a single delayed HIV-1 and discuss the effect of time delay in controlling HIV-1 infection. Once the complete dynamics of single delayed model is studied, we will extend this study to double delayed HIV-1 infection models. Incorporated time delays represent delay in contact process between pathogen virus and CD+4 cells (binding), latent period, virus production period and CTLs response. Then, to study the effect of dose-dependent infection rate in reducing HIV-1 infection, a new model is formulatedanditsstability willbediscussed. Themodelwillbeextendedbyincorporating the effect of recovery rate of unproductively infected cells to uninfected cells. Moreover, in order to reduce HIV-1 infection in the body, optimal control strategies will be developed. The aim of control strategies is to minimize the concentration of infected cells and maximize the concentration of uninfected cells. For this purpose optimal control variables will be incorporated in the proposed HIV-1 infection models with time delays and without time delays. To analyze the dynamical behavior of fractional order HIV-1 infection model, the proposed integer order HIV-1 models will be converted into fractional order model and its solution behavior will be discussed. Finally, to verify the derived theoretical results numerical simulations will be carried out for both integer and fraction order HIV-1 models.