Research Article A Mathematical Model for Coinfection of Listeriosis and Anthrax Diseases Shaibu Osman 1 and Oluwole Daniel Makinde 2 1 Department of Mathematics, Pan African University, Institute for Basic Sciences, Technology and Innovations, Box 62000-00200, Nairobi, Kenya 2 Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa Correspondence should be addressed to Shaibu Osman; shaibuo@yahoo.com Received 8 April 2018; Accepted 9 July 2018; Published 2 August 2018 Academic Editor: Ram N. Mohapatra Copyright © 2018 Shaibu Osman and Oluwole Daniel Makinde. 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. Listeriosis and Anthrax are fatal zoonotic diseases caused by Listeria monocytogene and Bacillus Anthracis, respectively. In this paper, we proposed and analysed a compartmental Listeriosis-Anthrax coinfection model describing the transmission dynamics of Listeriosis and Anthrax epidemic in human population using the stability theory of diferential equations. Our model revealed that the disease-free equilibrium of the Anthrax model only is locally stable when the basic reproduction number is less than one. Sensitivity analysis was carried out on the model parameters in order to determine their impact on the disease dynamics. Numerical simulation of the coinfection model was carried out and the results are displayed graphically and discussed. We simulate the Listeriosis-Anthrax coinfection model by varying the human contact rate to see its efects on infected Anthrax population, infected Listeriosis population, and Listeriosis-Anthrax coinfected population. 1. Introduction Listeriosis and Anthrax are fatal zoonotic diseases caused by Listeria monocytogene and Bacillus Anthracis, respectively. Listeriosis in infants can be acquired in two forms. Mothers usually acquire it afer eating foods that are contaminated with Listeria monocytogenes and can develop sepsis resulting in chorioamnionitis and delivering a septic infant or fetus. Moreover, mothers carrying the pathogens in the gastroin- testinal tract can infect the skin and respiratory tract of their babies during childbirth. Listeria monocytogenes are among the commonest pathogens responsible for bacterial meningitis among neonates. Responsible factors for the disease include induced immune suppression linked with HIV infection, hemochromatosis hematologic malignancies, cirrhosis, diabetes, and renal failure with hemodialysis [1]. Authors in [2] developed a model for Anthrax transmis- sion but never considered the transmissions in both animal and human populations. Our model is an improvement of the work done by authors in [2, 3]. Both formulated Anthrax models but only concentrated on the disease transmissions in animals cases only. Anthrax disease is caused by bacteria infections and it afects both humans and animals. Our model is an improvement of the two models as we considered Anthrax as a zoonotic disease and also looked at sensitivity analysis and the efects of the contact rate on the disease transmissions. Authors in [4] published a paper on the efectiveness of constant and pulse vaccination policies using SIR model. Te analysis of their results under constant vaccination showed that the dynamics of the disease model is similar to the dynamics without vaccination [5, 6]. Tere are some fndings on the spread of zoonotic diseases but a number of these researches focused on the efect of vaccination on the spread and transmission of the diseases as in the case of the authors in [7]. Moreover, authors in [8] investigated a disease transmission model by considering the impact of a protective vaccine and came up with the optimal vaccine coverage threshold required for disease eradication. However, authors in [9] employed optimal control to study a nonlinear SIR epidemic model with a vaccination strategy. Several mathematical modeling techniques have been employed to Hindawi International Journal of Mathematics and Mathematical Sciences Volume 2018, Article ID 1725671, 14 pages https://doi.org/10.1155/2018/1725671