Given the economic importance of advertising and product promotions, we have developed a diffusion model to describe the impact of advertising on sales. The main message of this study is to show the effect of advertising diffusion to convert potential buyers into actual customers which may result in persistent alteration in marketing over time. This work is devoted to studying the dynamic behavior of a reaction-diffusion model and its delayed version with the advertising effect. For the non-delay model, it is proven the existence of Hopf bifurcation. Moreover, the stability and direction of bifurcation of periodic solutions are detected. On the other hand, we consider there is a lag for responding of potential buyers to the advertising. Therefore, the time delay τ is deemed as an additional factor in the diffusion model. We have determined the critical values for the delay parameter that yield periodic solutions. Furthermore, the direction and the stability of bifurcating periodic solutions is studied. For supporting the theoretical analysis and demonstrate complex dynamic behaviors, numerical simulations including families of periodic curves are given.

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Background: Assessment of the students' opinion throughout their teaching course is a crucial part to achieve the intended learning outcome. Objectives: Were to assess and compare the students' attitude and perception towards basic medical sciences during the preclinical and clinical academic years, to recognize their opinion to early integration of both basic and clinical sciences, their preferred basic subjects and related causes. Subjects and Methods: A cross sectional study was conducted on 344 female medical students. They were randomly selected through the academic year 2015-2016, at the Faculty of Medicine for Girls, Al-Azhar University in Cairo. Data were collected using a valid and reliable (nine items) questionnaire. The first five items measured the perceived importance and relevance of basic medical sciences to clinical medicine, and the last four items measured students' attitudes towards, and perceived effectiveness of their education in basic medical sciences. Necessity of integration from the first year and the preferred basic medical subjects were also asked about. All opinions were rated using a three points Likert scale. Results: A significant difference between the two groups was obtained as regards that "physician can effectively treat most medical patients without knowing the details of the biological processes (72.4% versus 75.9%). While, disagreement perception was significantly higher among clinical group students (62.8%) compared to preclinical students (47.8%) as regards less value of basic medical sciences in clinical practice. Modest agreement attitude was the dominant towards the further statements with no significant difference (p>0.005). How best to integrate both clinical and basic medical sciences was not significant and represented 67.5% and 71.0% among preclinical and clinical students respectively. The top preferred basic medical sciences were; anatomy, physiology and pathology. Understandable curriculum, good professor and clear method of teaching were the main causes for preference. Conclusion and Recommendation: Overall positive attitude and perception towards basic medical sciences are found, mainly among students in clinical years. Refocusing the basic/clinical medical sciences is essential to cross the gap between knowledge and medical practice. Opinion of the students is necessary to be considered to provide the educational planners with valuable guidelines in order to maximize the benefits of medical curricula and prepare medical students efficiently for clinical work. Further studies prior to the application of the integrated program are required.

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