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  • Küçük Resim
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    Local Stability of Dengue Model Using the Fractional Order System with Different Memory Effect on the Host and Vector Population
    (VINCA INST NUCLEAR SCI, MIHAJLA PETROVICA-ALASA 12-14 VINCA, 11037 BELGRADE. POB 522, BELGRADE, 11001, SERBIA, 2019) Hamdan, Nur 'Izzati; Kılıçman, Adem
    In this study, we formulate a fractional order dengue model by considering different order dynamics on human and mosquito population. The order of the differential equation is associated with the index of memory. Both human and mosquito carry a different value of order to showcase the different memory effect implies to each of them in the transmission process. Local stability of the equilibria is obtained based on the threshold parameter related to the basic reproduction number; denoted by R-0. Finally, numerical simulations of the model are conducted to study the dynamical behavior of the system.
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    Sensitivity Analysis in a Dengue Fever Transmission Model: A fractional order system approach
    (IOP PUBLISHING LTD, DIRAC HOUSE, TEMPLE BACK, BRISTOL BS1 6BE, ENGLAND, 2019) Hamdan, Nur 'Izzati; Kılıçman, Adem
    The main purpose of the study of dengue fever transmission is to be able to determine the best approach to reduce human mortality and morbidity caused by the disease. Therefore, it is essential to identify the relative importance of the different factors that contribute to disease transmission and prevalence. Here, a fractional order epidemiological model describing the dengue fever transmission is presented, as well as the basic reproduction number, denoted by R0. The initial disease transmission is highly significant with the basic reproduction number, R0. Thus, the needs for conducting an analysis that tells us how sensitive the threshold quantity of R0 is, with respect to its parameters, is very crucial. The sensitivity analysis is performed to calculate the sensitivity indices of the reproduction number R0, that measures the disease transmission and the endemic equilibrium point, that measures disease prevalence to the parameters model. It has been shown that for the reproduction number, the most sensitive parameters are the mortality rate of the adult mosquito and the mosquito biting rate. However, the equilibrium proportion of infected humans is very sensitive to the transition rate from the immature vector stage to the adult stage, and human recovery rate. These suggest that dengue control policies that target the vector population and recovery rate of individuals can be a great resolution in controlling dengue.