دانلود مقاله تعمیم مدل بیماری عفونی بر اساس اغتشاشات دمایی بدن
چکیده
مقدمه
مرور مطالعات پیشین
مطالب و روش ها
آزمایش های عددی
نتایج و بحث
نتیجه گیری
منابع
Abstract
Introduction
Literature reviews
Methods
Numerical experiments
Results and discussion
Conclusions
References
چکیده
مدل ریاضی بیماری عفونی بر اساس تأثیر اغتشاشات منتشر در توسعه بیماری تحت شرایط واکنش دمای بدن تعمیم می‌یابد. مشکل مدل تکین آشفته با تاخیر به دنباله ای از مسائل بدون تاخیر کاهش یافت، که برای آن بسط مجانبی مربوط به راه حل ها به دست می آید. نتایج ارائه‌شده از مدل‌سازی رایانه‌ای در حالت‌های موقعیتی مختلف، کاهش مورد انتظار در نرخ رشد تعداد ذرات ویروسی را در نتیجه عمل واکنش دمای محافظ بدن نشان می‌دهد. نتایج آزمایش‌های عددی نشان می‌دهد که تأثیر انتشار "پراکندگی" عوامل اجباری بر پویایی یک بیماری ویروسی در شرایط واکنش دمای بدن نیز ارائه شده است. خاطرنشان می شود که کاهش مقدار مدل آنتی ژن ها در مرکز عفونت به سطح غیر بحرانی ناشی از "پراکندگی" منتشر در یک دوره زمانی نسبتاً کوتاه باعث می شود که آنها توسط عوامل ایمنی ارائه شده در بدن بیشتر از بین بروند یا نیاز به معرفی یک محلول تزریقی با مقدار کمتری از آنتی بادی های دهنده.
توجه! این متن ترجمه ماشینی بوده و توسط مترجمین ای ترجمه، ترجمه نشده است.
Abstract
The infectious disease mathematical model is generalized based on the influence of diffuse perturbations on the development of the disease under conditions of the body's temperature reaction. The singularly perturbed model problem was reduced with delay to a sequence of problems without delay, for which the corresponding asymptotic expansions of solutions are obtained. The presented results of computer modeling in various situational states illustrate the expected decrease in the growth rate of the number of viral particles as a result of the action of the body's protective temperature reaction. The results of numerical experiments demonstrate the influence of the diffuse effect of “scattering” of forcing factors on the dynamics of a viral disease under conditions of the body's temperature reaction are presented too. It is noted that the decrease of the model amount of antigens in the epicenter of infection to a non-critical level caused by diffuse “scattering” over a relatively short time period makes them further destroyed by immune agents presented in the body, or requires the introduction of an injection solution with a smaller amount of donor antibodies.
Introduction
Modern concepts of the host's reaction to the identified pathogens indicate the existence of a complex system of dissimilar and interrelated immune defense mechanisms. Mathematical models of immune processes are the integral and important elements in the research of these mechanisms. The number of mathematical models of various levels of details were proposed in Ref. [1] to research and predict the process of interaction of the immune system with the pathogens found in the host. These models are based on the clonal selection theory of F. Burnet [1,2]. The most general patterns of the immune response are studied on the basis of the so-called infectious disease simplest model, which is represented by a system of four nonlinear differential equations with delay. In particular, the asymptotic stability of the stationary solution is substantiated, which describes the healthy body's state if the initial infection dose of some immunological barrier is not exceeded. That is, when a healthy host is infected with small dose of viral particles, their neutralization according to the model is provided by available amount of antibodies. Moreover, the included certain variability in the simplest model makes it possible to explain some important features functioning of the immune system. Besides, this allows explaining the possibility of the formation of subclinical, acute and chronic processes of the disease and clarifying the mechanisms of biostimulation, etc. [1]. The improved mathematical models of antiviral and antibacterial immune response are proposed for taking into account the immunity of the T-cell type in Ref. [1]. These models include the mechanism of the humoral immune response with the production of antibodies and the mechanism of recognition and destruction by cytotoxic T-lymphocytes-effectors accumulated as a result of the immune response of the cells of their own body infected with the virus.
Conclusions
The presented approach takes into account the influence of diffuse perturbations and different kinds of concentrated influences on process development under conditions of a body's self-protective temperature reaction is presented on the basis of mathematical model generalization of infectious disease. The solution singularly perturbed model problem with delay is introduced as sequence of problems without delay for which additional consistency conditions are determined that ensure the smoothness required order. The asymptotic method is applied to find solutions of problems at each time step, that makes it possible to construct an efficient computational procedure, according to which the known basic “unperturbed” solutions are supplemented by various corrections.