A FUZZY MEASLES EPIDEMIC MODEL, GENERALIZED APPROACH IN A FUZZY ARITHMETIC FRAMEWORK
A FUZZY MEASLES EPIDEMIC MODEL, GENERALIZED APPROACH IN A FUZZY ARITHMETIC FRAMEWORK

Summary/Abstract: The epidemiological models modelled by a system of differential equation depending of time are useful to model the dynamic of the epidemic along with future prediction of the spread of disease. Also, the dynamic model help to better understand the equilibrium point(s) and when is the case the optimal strategy for vaccination (where the vaccination is possible and a vaccine exists) or treatments allow eventually with other measures (as social education in some cases). One of the most studied models that can apply for many diseases that are described by compartmental model is the SEIR model: malaria, Ebola, measles, etc. There are few proposals for simulation tools of epidemic models but all are for crisp cases. In this paper we propose an educational tool for simulation of fuzzy SEIR model applicable to measles dynamics where all the coefficients from model can be crisp numbers of fuzzy numbers (triangular, trapezoidal or Gaussian) with corresponding graph display of epidemic dynamics. Moreover, in the cases when two coefficients are in the same differential equation, a proposal to solve to problem is made in the fuzzy arithmetic network. An additional module is used to construct a more extended fuzzy epidemiologic model, with additional compartment, e.g. SEIRS, in a friendly manner by a user interface for builder model of differential equations. The tool has a library with predefined models and an option to select to parameters in order to have an asymptotic stable solution. The user can select the graphs to be displayed on the common window or in a separated window with zooming possibility to evaluate better the evolution of dynamic system.

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