Epidemic model in a population with Allee effect using fuzzy approach
Z Amarti (a*), N Anggriani (a), E D Wiraningsih (b), A K Supriatna (a)

(a) Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, INDONESIA
*zeniamarti[at]gmail.com
(b) Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Jakarta, INDONESIA

Abstract

Epidemiology has been defined as the study of disease distribution and its determinants in human population. The epidemic growth model is an important tools used in preparing good management for society to predict the future of the population and the spread of disease. Epidemic models are usually formed in differential equations or systems of differential equations, depending on the complexity of the underlying properties of the population. One example of biological complexity is the Allee effect. In this paper we discuss a Logistic epidemic by considering the Allee effect on the population. Dynamic analysis is performed by determining fixed point and its stability analysis in crisp condition. We found the Basic Reproduction Ratio (BRR) for the model. The properties of the solution of the model are explored by the use of its numerical solution. The numerical solution is obtained using the Runge-Kutta method. Further exploration is done through a fuzzy theory approach to accommodate uncertainty, inaccuracy and uncertainty in epidemiological problems.

Keywords: Logistic epidemic model; Allee effect; Fuzzy theory

Topic: Mathematics