Cholera is an extremely virulent disease. It has long been, and continues to be, a world health issue. It affects both children and adults and can kill within hours. During the 19th century, cholera spread across the world from its original reservoir in the Ganges delta in India [23]. There have been seven great pandemic (worldwide epidemics) of cholera in history. The seventh began in 1961, when cholera re-emerged in Indonesia and swept across most of the world, reached Africa in 1971 and the Americas in 1991, and still lingers today [5]. At the beginning of the 21st century, cholera infected around 300,000 people per year worldwide; of these, about 10,000 died [24]. For instance, from August 2008 to February 2009, more than 79,000 cases and 3,700 deaths were reported from a single country, Zimbabwe. Regardless of the advancement of medical science and health care service, cholera remains a global threat to public health and one of the key indicators of social development.
Cholera is an acute intestinal infection caused by ingestion of food or water contaminated with the bacteria Vibrio cholerae [5,18]. V. cholerae is a motile gram-negative curved-rod bacterium with polar flagellum that causes cholera in humans. The bacteria is typically found in water environments such as freshwater lakes and rivers. The bacterium that causes cholera is usually transmitted by water contaminated with human feces, but it can also be transmitted by ingesting contaminated food, especially raw or undercooked seafood and shellfish. Most people infected with cholera have no symptoms, yet they carry the bacteria for a few weeks, excreting them slowly into the water supply.
Mathematical models for cholera are relatively recent. In 1979, Capasso and Paveri-Fontana proposed a mathematical model to describe the 1973 cholera epidemic in Bari (a city in Italy) [1]. In Capasso's version, two equations describe the dynamics of infected people in the community and the dynamics of the aquatic population of pathogenic bacteria. In 2001, Codeco [3] extended the model of Capasso and Paveri-Fontana. He added an equation for the dynamics of the susceptible population. And, he studied the role of the aquatic reservoir in the endemic-epidemic dynamics of cholera. In [17], Pascual et al. generalized Codeco's model by including a fourth equation for the volume of water in which the formative live following Codeco [3]. In 2009, Joh et al. considered the dynamics of infectious diseases for which the primary mode of transmission is indirect and mediated by contact with a contaminated reservoir [11]. To the best of our knowledge, these studies do not explicitly consider a deterministic compartmental model with vaccination.
Cholera vaccine given by injection may help prevent cholera. Cholera vaccine is not available as part of the schedule; however, persons who are at an increased risk for cholera infection (for example, travelers to a cholera-endemic country, persons living in conditions where sanitation is poor and the risk of cholera is high, refugees of a camp where the possible outbreak of cholera is high) should be vaccinated. The aim of cholera vaccination is to reduce the case fatality rate to less than 1%. There are two types of cholera vaccines: