Mathematical Modeling of Dengue Disease under Random Effects

Abstract

In this study, the deterministic mathematical model of Dengue disease is examined under Laplacian random effects. Random variables with Laplace distribution are used for randomizing the deterministic parameters. Simulations of the numerical results of the equation system are made with Monte-Carlo methods and the results are used for commenting on the disease. Comments are made on the random behavior of the components of the model after the calculation of their numerical characteristics like the expected value, variance, standard deviation, confidence interval and moments along with the coefficients of skewness and kurtosis from the results of the simulations. Results from the deterministic model are compared with the results from the random model to point out the possible contribution of random modeling to mathematical analysis studies on the disease.

Diferansiyel Dönüşüm Yöntemi İle Rastgele Kalp Atış Modelinin Analizi

“…The parameters of the differential equation system will be added random effects with Gaussian (normal) and beta distribution to represent the natural fluctuations in the dynamics of heartbeat. Similar modeling studies have been made with random effects for bacterial resistance and biochemical reactions [2,6] .…”

Analysis of The Dynamics of The Classical Epidemic Model with Beta Distributed Random Components

“…The parameters of system (2) will be transformed into random variables with symmetrical general Beta distribution to model the randomness of the values of recovery and contact rates in real life. The expected value of a general Beta distributed random variable * with parameters ( , , , ) is given as (Bekiryazici et al, 2016)…”