A Mathematical Model For The Transmission Dynamics Of Influenza With Respect To Seasonal Weather Variables In Kenya

Abstract

The aim of this project is to carry out a research on the e ects of weather variables on the seasonality of in uenza. For this purpose we formulate a compartmental model to represent in uenza transmission dynamics. In uenza is modeled as a 5-dimensional deterministic system of ODE’s with a variable transmission rate expressed as an exponential function of the weather variables. The basic properties including the basic reproduction number are derived. The disease free and endemic equilibrium of the model are found and their stability analyzed. The disease free equilibrium point is found to be both locally and globally stable. In uenza data was organized into seasons from December 2006 to November 2011. Graphs were drawn for all the four stations to determine the season with the most u prevalence. It was established that, the 3rd season has the most u prevalence while the 1st season had the least u prevalence. The mean values of the weather variables were retrieved from world weather website online and aggregated into seasonal values. The correlation coe cient of u with the basic reproduction number, temperature, rainfall and humidity was calculated. In Nairobi station, we see that there is a positive correlation between u and the basic reproduction number. In all the four stations, we can see that there is a negative correlation between u and temperature and u and rainfall. On the other hand, there is a positive correlation between u and humidity.