On the spread of epidemics in a closed heterogeneous population.

نویسنده

  • Artem S Novozhilov
چکیده

Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptible-infective-removed) model is formulated and analyzed when susceptibility to or infectivity of a particular disease is distributed. It is shown that a heterogeneous model can be reduced to a homogeneous model with a nonlinear transmission function, which is given in explicit form. The widely used power transmission function is deduced from the model with distributed susceptibility and infectivity with the initial gamma-distribution of the disease parameters. Therefore, a mechanistic derivation of the phenomenological model, which is believed to mimic reality with high accuracy, is provided. The equation for the final size of an epidemic for an arbitrary initial distribution of susceptibility is found. The implications of population heterogeneity are discussed, in particular, it is pointed out that usual moment-closure methods can lead to erroneous conclusions if applied for the study of the long-term behavior of the models.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Impact of Geographical Factors on the Prevalence of Pervasive Diseases in Guilan, Qajar Era in Perspective of European Tourists

European tourists in their reports from Guilan in the Qajar era, also have addressed the issue of health and deadly diseases affecting lives of people, such as rice fever, malaria, cholera, and plague in addition to pointing out the numerous social tragedies. From these tourists’s point of view, the weather conditions, geographical location, livelihood and some living and social habits and beha...

متن کامل

Transmission of Epidemic Diseases through the Persian Gulf In the Late Thirteenth and Early Fourteenth Century AH

In the late 13th and early 14th centuries, Iran was involved with epidemics such as plague and cholera, affecting the population and economy of the country. The spread of these diseases, on the one hand, was the result of the government's inability to organize health centers and, on the other hand, the inability to prevent these diseases by the quarantine of the borders. The southern borders of...

متن کامل

A new mathematical model for the closed-loop supply chains considering pricing for product, a fleet of heterogeneous vehicles, and inventory costs

Mathematical models have been used in many areas of supply chain management. In this paper, we present a mixed-integer non-linear programing (MINLP) model to solve a multi-period, closed-loop supply chains (CLSCs) with two echelons consist of producers and customers. In order to satisfy the demands, the producers are be able to order for materials in the beginning of each period for one or more...

متن کامل

Adaptive Distributed Consensus Control for a Class of Heterogeneous and Uncertain Nonlinear Multi-Agent Systems

This paper has been devoted to the design of a distributed consensus control for a class of uncertain nonlinear multi-agent systems in the strict-feedback form. The communication between the agents has been described by a directed graph. Radial-basis function neural networks have been used for the approximation of the uncertain and heterogeneous dynamics of the followers as well as the effect o...

متن کامل

عوامل مؤثر بر همه‌گیری شیگلا فلکسنری در شهر اصفهان در سال 1394: مطالعه مورد- شاهدی

Background and Objectives: Epidemics of diarrhea caused by contaminated food and water occur frequently worldwide, especially in developing countries. The aim of this study was to identify the factors contributing to the development and spread of diarrhea epidemics caused by Shigella  flexneri  in Isfahan in the spring of 2015.   Methods: Following the first reports and activation of the surv...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Mathematical biosciences

دوره 215 2  شماره 

صفحات  -

تاریخ انتشار 2008