A new fractional modelling and control strategy for the outbreak of dengue fever

Amin Jajarmi, Sadia Arshad and Dumitru Baleanu

Physica A: Statistical Mechanics and its Applications, 2019, vol. 535, issue C

Abstract: This paper deals with a new mathematical model for a dengue fever outbreak based on a system of fractional differential equations. The equilibrium points and stability of the new system are studied. To simulate this model, a new and efficient numerical method is provided and its stability and convergence are proved. According to a real outbreak on the Cape Verde Islands occurred in year 2009, the new model is examined for a period of three months by using singular or nonsingular kernels in the definition of derivative operator. Simulation results show that the proposed formalism with exponential kernel agrees well with the real data in the early stage of the epidemic while the Mittag-Leffler kernel fits the reality for the later part of the time interval. Hence, the new framework in a hybrid manner can properly simulate the dynamics of the disease in the whole of the time interval. In order to stabilize the disease-free equilibrium point of the system under investigation, two control strategies are suggested. Numerical simulations verify that the proposed stabilizing controllers are efficient and provide significantly remarkable results.

Keywords: Dengue model; Fractional derivative; Nonsingular kernel; Trapezoidal method; Stabilizing controller (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (34)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:535:y:2019:i:c:s0378437119314451

DOI: 10.1016/j.physa.2019.122524

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