Fuzzy SEIR Epidemic Model of Amoebiasis Infection in Human

Abstract

Amoebiasis is a disease caused by the protozoan Entamoeba histolytica. It is often asymptomatic but may cause dysentery and invasive extraintestinal infection in humans. To gain an understanding of the disease, a fuzzy SEIR model of amoebiasis infection is presented with the fuzziness introduced in the disease transmission rate, the disease-induced death rate, and the rate of recovery from infection. The basic reproduction number ${\mathrm{ℛ}}_0\left(v\right)$ is computed and used to make a comparison with the fuzzy basic reproduction number ${\mathrm{ℛ}}_0^f$ at different amounts of cysts as well as to analyse the stability of equilibrium points. Stability results indicate that the disease-free equilibrium and the endemic equilibrium are locally and globally asymptotically stable. Further, numerical simulations are carried out to illustrate the analytical results of the fuzzy model system. The result shows that whenever there is an outbreak, the disease is likely to persist in the first month and thereafter it will start to slow down to disease-free equilibrium.