Mathematical Theory and Modeling www.iiste.org ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online) DOI: 10.7176/MTM Vol.9, No.6, 2019 45 Mathematical Modeling and Stability Analyses of Lassa Fever Disease with the Introduction of the Carrier Compartment Mary Oluwabunmi Akinade 1∗ , Ayodeji Sunday Afolabi 2 , Mark Eric Kimathi 3 1. Department of Computational Mathematics, Pan African University Institute for Basic Sciences, Technology and Innovation (PAUSTI), P.O. Box 62000-00200, Nairobi-Kenya 2. Department of Mathematical Sciences, Federal University of Technology Akure (FUTA), P.M.B. 704, Akure, Ondo State, Nigeria 3. Department of Mathematics and Statistics, Machakos University (MKsU), P.O Box 136-90100, Machakos-Kenya * E-mail of the corresponding author: akinademary18@gmail.com Abstract In this paper, a new mathematical model which takes into account the human and vector populations together with their interactions during Lassa fever disease transmission was developed. This transmission process is denoted by a seven mutually exclusive compartments for the human and vector populations. The proposed model is used to introduce the incubation period of the disease, a period in which an infected individual is yet to be symptomatic but infectious however, as denoted by the carrier human compartment. This carrier compartment was critically examined for its short and long term effects on the spread and control of the disease. Local and global stability analyses of the equilibrium points of the model was carried out using the first generation matrix approach and the direct Lyapunov method respectively. These analyses showed that the disease free equilibrium point of the developed model is locally asymptotically stable but not globally asymptotically stable. It was also observed that, although, there exist a unique endemic equilibria for the disease, this equilibria however is not stable. Numerical simulations of the model were carried out by implementing the MATLAB ODE45 algorithm for solving non-stiff ordinary differential equations. The results of these simulations are the effects of the various model parameters on each compartment of the developed model. Based on the findings of this research, necessary recommendations were made for the applications of the model to an endemic area. Keywords: Mathematical Model, Stability Analyses, Lassa Fever, Equilibrium Points, Numerical Simulation. DOI: 10.7176/MTM/9-6-04 Publication date: June 30 th 2019 1. Introduction Lassa Fever (LF) is a fatal acute Viral Hemorrhagic fever caused by Lassa Virus (LASV). LASV belongs to the arena-virus family of viruses and the major host of this virus is the Mastomys (atalensis) rat specie. In addition to Person to person transmission, the other major form of transmission of the disease is from an infected animal(s) to humans. Laboratory transmission in hospitals lacking appropriate infection prevention and control measures is also common. The first occurrence of Lassa fever was in a town called "Lassa" in the present Borno state of Nigeria in 1969 and this was how the name "Lassa fever" was given to the disease. The first victim of the disease was a 65 year old female nurse who worked at the Lassa mission hospital, presently known as "Bingham University Teaching Hospital", in Borno state, Nigeria. Subsequently, the disease has been greatly spreading in Africa. Currently, there has been an outbreak of LF in many west African countries, such as Sierra Leone, Liberia, Guinea and Nigeria, with an increasing fatal rate. The fatality rate in symptomatic, hospitalized patients ranges from 15% to 20% and as high as 90% in pregnant women [10]. There has been more outbreak of LF disease in Nigeria than in every other countries in which the disease has ever been reported. Among the 413 confirmed Lassa fever cases in Nigeria between 1st day of January and the 15th day of April 2018, 114 deaths were reported [23]. The 2018 LF outbreak in Nigeria was the largest recorded outbreak of the virus with about 1,400 suspected cases and more than 300 confirmed cases between April and June 2018 [11]. Other incidences of Lassa fever appear to be in areas of eastern sierra Leone, south-eastern Guinea, and northern Liberia. [21] reported that a total of 128 contacts, including 59 health care workers, have been line-listed and were being followed up in Liberia in June, 2018. Two deaths were reported in this outbreak. The release also disclosed that, although LF is not new to Liberia, brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by International Institute for Science, Technology and Education (IISTE): E-Journals