| Summary: In this study, the deterministic mathematical model of Dengue disease is examined under Laplacian random effects. Dengue disease is a tropical disease transmitted by a special type of mosquitoes. Dengue disease is modeled bu using nonlinear deterministic differential equations in the literature. However, it is known that some of the parameters used in the mathematical modeling of Dengue disease are dependent on external factors. Hence, the parameters of the equation system used for the modeling the transmission of dengue fever should be randomized by using random effect terms. This way, the randomness in the events described by the randomized parameters can be modeled in the equation system. Random variables with Laplace distribution are used for randomizing the deterministic parameters. The behavior of dengue fever disease is examined with a model consisting of nonlinear random differential equations. 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 calculating 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 the mathematical analysis studies on the disease. The used random modeling studies are innovative for dengue fever and will contribute to the mathematical studies on dengue fever.
Key Words: Mathematical Model, Random Effect, Simulation, Laplace Distribution.
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