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

作     者：Josephine Wairimu Sallet Gauthier Wandera Ogana 

作者机构：INRIA Metz and University of Lorraine Metz France School of mathematics University of Nairobi Nairobi Kenya 

出 版 物：《Applied Mathematics》 (应用数学（英文）)

年 卷 期：2014年第5卷第10期

页      面：1535-1545页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Highland Malaria Differentiated Susceptibility and Infectivity Monotone Dynamical Systems Age Structure 

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.