SUATU ANALISIS DARI MODEL MATEMATIKA PENYAKIT KOLERA ( AN ANALYSIS OF CHOLERA DISEASE MODEL )

Fitriyah, Aini, Sumardi

2015 | Disertasi | FMIPA

In this paper, two mathematical models of cholera are analyzed. The models consist of person-to-person and water-to-person transmission routes. First, a single infected compartment model, in terms of its basic reproduction number (R0) if R0 < 1 the disease-free equilibrium is globally asymptotically stable and the infection will disappear. Whereas if R0 > 1, the unique endemic equilibrium is also globally asymptotically stable and the infection will be endemic to the population. Second, a multiple infected compartments model, it consists of three stages of cholera infection. In terms of its basic reproduction number (R0), if R0 < 1 the disease-free equilibrium is globally asymptotically stable and the infection will disappear. Whereas if R0 > 1, the unique endemic equilibrium is also globally asymptotically stable if lifetime of pathogen is short. Numerical simulations verify the theoretical results and present that the decay rate of pathogens has a significant impact on the epidemic growth rate if R0 > 1. The simulations also show that the unique endemic equilibrium is asymptotically stable for the different lifetime of the pathogen.

Kata Kunci : Cholera, person-to-person, water-to-person, single infected compartment, multiple infected compartments; stability of equilibrium point; basic reproduction number.