# Dr. Josephine Wairimu

## BSc, (Egerton), MSc, (Nairobi), PhD, (Univ. of Lorraine) Applied Mathematics

Email: jwndirangu@uonbi.ac.ke

Email: jwndirangu@uonbi.ac.ke

- Citation:
- Wairimu J, Sallet G, Ogana W. "Formulation of a vector SIS malaria model in a patchy environment with two age classes." Scientific Research Publishing. 2014;5(10):1535-1545.

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 susceptibili-ty 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 n 3 . 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 circula-tion of malaria parasites among the species and among the patches is strongly connected, hence transmission is sustained. We show that for the n-dimensional age structured system the positive orthant is positively invariant for all positive values of the variables.