BioSystems 105 (2011) 190–200 Contents lists available at ScienceDirect BioSystems jo ur nal homep age : www.elsevier.com/locate /biosystems Mathematical analysis of a cholera model with public health interventions A. Mwasa a , J.M. Tchuenche b,∗ a Department of Mathematics, Islamic University in Uganda, Mbale, Uganda b Mathematics Department, University of Dar es Salaam, Dar es Salaam, Tanzania a r t i c l e i n f o Article history: Received 4 January 2011 Received in revised form 31 March 2011 Accepted 1 April 2011 MSC: 92B05 92D30 92C50 93D05 93D20 Keywords: Cholera Educational campaign Vaccination Treatment Reproduction number Stability a b s t r a c t Cholera, an acute gastro-intestinal infection and a waterborne disease continues to emerge in developing countries and remains an important global health challenge. We formulate a mathematical model that captures some essential dynamics of cholera transmission to study the impact of public health educational campaigns, vaccination and treatment as control strategies in curtailing the disease. The education- induced, vaccination-induced and treatment-induced reproductive numbers R E , R V , R T respectively and the combined reproductive number R C are compared with the basic reproduction number R 0 to assess the possible community benefits of these control measures. A Lyapunov functional approach is also used to analyse the stability of the equilibrium points. We perform sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. Graphical representations are provided to qualitatively support the analytical results. © 2011 Elsevier Ireland Ltd. All rights reserved. 1. Introduction Cholera is an acute diarrhoeal illness caused by infection of the intestine with the bacterium Vibrio cholerae (V. cholerae). The infection is often mild or without symptoms, but sometimes it can be severe. Infected persons may develop severe disease char- acterized by profuse watery diarrhoea, vomiting, leg cramps and if untreated, it leads to rapid dehydration, acidosis, circulatory collapse and death within 12–24 h (Sanchez et al., 1994; WHO, 2008). V. cholerae is naturally found in aquatic plankton, partic- ularly copepods. Drinking water from copepod-infested sources causes the disease (Qu et al., 2003). The risk factors for cholera are varied and stem from multiple transmission pathways, including but not limited to indirect transmission through the environ- ment, e.g., from food and water contamination (Epstein et al., 1993; Kaper et al., 1995). V. cholerae was first isolated as the cause of cholera by the Italian anatomist Filippo Pacini in 1854. V. cholerae serotype 01 was considered the sole etiologic agent of epidemic and pandemic cholera, until October 1993, when a non- 01 serotype of V. cholerae referred to as V. cholerae 0139 or the ∗ Corresponding author. E-mail addresses: a.mwasa@yahoo.com, jmtchuenche@gmail.com (J.M. Tchuenche). “Bengal” strain appeared in Chennai, India with a serious epidemic potential (Ramamurthy et al., 1993). Since that time, V. cholerae 01 and 0139 serotypes have both been considered the etiologic agents of epidemic cholera (Sea and Gotuzzo, 1996). Both serotypes are natural habitants of the estuarine environment (ocean bays) and cause cholera disease through consumption of contaminated seafood. Cholera is transmitted through ingestion of faecal matter contaminated with the bacterium (Faruque et al., 2005; Jensen et al., 2006; Rivera, 2003). Millions of people throughout the world, especially in developing countries, have little access to sanitary waste disposal infrastructure or clean potable water. Cholera vac- cine offers at least 85–90% protection during six months in all age groups after administration of two doses, one week apart. Despite its availability, affordability remains the greatest drawback. In 2002, 52 nations reported 142,311 cholera cases and 4564 deaths. These statistics probably represent a small subset of the actual cases and deaths globally due to poor surveillance and underreporting (WHO, 2008). Cholera outbreaks have been occurring sporadi- cally in developing countries – Kisangani and Ubundu districts, Democratic Republic of Congo in 2007 – Angola (UNICEF, 2008) – Zanzibar and Dar es Salaam, Tanzania – Co Guinea-Bissau – Butaleja, Uganda, Kenya (WHO, 2008) – Zimbabwe experienced a sharp rise in acute child malnutrition leading to a worsening cholera epidemic in 2008–2009 (Mason, 2009), and more recently in 0303-2647/$ – see front matter © 2011 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.biosystems.2011.04.001