Research Article The Effect of Seasonal Weather Variation on the Dynamics of the Plague Disease Rigobert C. Ngeleja, 1 Livingstone S. Luboobi, 1,2 and Yaw Nkansah-Gyekye 1 1 Nelson Mandela African Institution of Science and Technology (NM-AIST), Arusha, Tanzania 2 Department of Mathematics, Makerere University, P.O. Box 7062, Kampala, Uganda Correspondence should be addressed to Rigobert C. Ngeleja; rngeleja@yahoo.com Received 21 February 2017; Accepted 28 June 2017; Published 10 August 2017 Academic Editor: Ram N. Mohapatra Copyright © 2017 Rigobert C. Ngeleja et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Plague is a historic disease which is also known to be the most devastating disease that ever occurred in human history, caused by gram-negative bacteria known as Yersinia pestis. Te disease is mostly afected by variations of weather conditions as it disturbs the normal behavior of main plague disease transmission agents, namely, human beings, rodents, feas, and pathogens, in the environment. Tis in turn changes the way they interact with each other and ultimately leads to a periodic transmission of plague disease. In this paper, we formulate a periodic epidemic model system by incorporating seasonal transmission rate in order to study the efect of seasonal weather variation on the dynamics of plague disease. We compute the basic reproduction number of a proposed model. We then use numerical simulation to illustrate the efect of diferent weather dependent parameters on the basic reproduction number. We are able to deduce that infection rate, progression rates from primary forms of plague disease to more severe forms of plague disease, and the infectious fea abundance afect, to a large extent, the number of bubonic, septicemic, and pneumonic plague infective agents. We recommend that it is more reasonable to consider these factors that have been shown to have a signifcant efect on   for efective control strategies. 1. Introduction Plague is the ancient disease caused by the bacterium Yersinia pestis and has had signifcant efects on human societies throughout the history [1]. Dynamics of plague disease are the result of complex interactions between human beings, rodent population, fea population, and pathogens in the environment. Seasonal variation particularly temperature, humidity, rainfall, and precipitation greatly afects the normal transmission capacity of plague disease by either lowering it or raising it. It afects pathogen in the environment, feas, rodents, and even human behavior by altering their normal immigration rate, death rate, survival rate, and infectious capability [2]. 1.1. Seasonality in Flea Development Stages and Behavior. Flea’s survival is greatly afected by temperature and relative humidity [3]. Te ectothermic characteristics of feas make them very sensitive to temperature fuctuations. Xenopsylla cheopis is the primary vector fea for Yersinia pestis. It is signifcantly afected by seasonal weather variation as most of its life stages depend on temperature, humidity, and precipitation. Te rate of metamorphosis of this kind of fea from egg to adult is also regulated by temperature. Flea larvae feed on almost any organic debris but mostly they feed on adult excreta which consist of relatively undi- gested blood [4]. Tis adult fecal matter when dried falls from the host to serve as food for the larvae. Tus the availability of food (dried fea dirt) for larvae to feed depends on the weather condition particularly temperature and humidity. Te larvae develop well in areas where the relative humidity is greater than 75 percent and the temperature is between 21 ∘ C and 32 ∘ C [5, 6]. At constant temperature feas become most sensitive to air saturation and are massively killed when the air saturation is insufciency [7]. Considering the fact that all immature fea stages occur outside the host, Hindawi International Journal of Mathematics and Mathematical Sciences Volume 2017, Article ID 5058085, 25 pages https://doi.org/10.1155/2017/5058085