Formulation of a Vector SIS Malaria Model in a Patchy Environment with Two Age Classes

• 作者: Josephine Wairimu Sallet Gauthier Wandera Ogana
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Highland MALARIA DIFFERENTIATED SUSCEPTIBILITY and Infectivity MONOTONE DYNAMICAL Systems Age Structure
• 年，卷（期）: 2014,（10）
• 页码范围: 1535-1545
• 页数: 11页
• 分类号: O1

摘要

We formulate an SIS model describing transmission of highland malaria in Western Kenya. The host population is classified as children, age 1- 5 years and adults, above 5 years. The susceptibility and infectivity of an individual depend on age class and residence. The large scale system with 6n equations is reduced into a compact form of 3n equations by a change of variables. Then 3n equations are vectorialized using the matrix theory to get a one dimension, compact form of the system, equation in . Using Vidyasagar theorem?[1], the graph of the reduced system is shown to be strongly connected and the system is a monotone dynamical system. This means that circulation of malaria parasites among the species and among the patches is strongly connected, hence transmission is sustained. We show that for then-dimensional age structured system the positive orthant is positively invariant for all positive values of the variables.