QUALITATIVE AND QUANTITATIVE ANALYSES OF THE DYNAMICS OF A VECTOR-BORNE DISEASE USING A FRACTIONAL FRAMEWORK

Rashid Jan, Normy Norfiza Abdul Razak (), Asma Alharbi and Salah Boulaaras
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Rashid Jan: Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya, Campus, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia†Mathematics Research Center, Near East University, TRNC, Mersin 10, Nicosia 99138, Turkey
Normy Norfiza Abdul Razak: Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya, Campus, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia
Asma Alharbi: Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia
Salah Boulaaras: Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 06, 1-18

Abstract: Vector-borne diseases pose substantial risks to public health and have a high impact on different sectors of life around the world. Hence, it is valuable to construct a conceptual framework for comprehending the dynamics of these infections to introduce efficacious public health control strategies. In this paper, we structure a model for a vector-borne infection to conceptualize the complex dynamics of dengue, including drug resistance and insecticide. The recommended model of dengue fever is presented through a non-integer derivative to capture the role of memory, drug resistance and insecticide. We examine the positivity and boundedness of the solution using analytic skills and the threshold parameter is determined via the next-generation matrix approach. The well-known theorem of fixed-point is utilized to evaluate the solution’s existence and uniqueness. We have provided sufficient conditions for the Ulam–Hyers stability. To delve further into the intricacies, we employ a numerical technique to elucidate how various input factors influence the infection dynamics. The impact of fractional-order parameters, vaccination rates, the rate of immunity waning, biting rates, resistance to drugs and insecticides is visualized. Our analysis has underscored the pivotal significance of certain parameters of the system, which can exert substantial influence over the intensity of dengue fever. In contrast, our findings suggest that parameters such as vaccination rates, the memory index, and fractional order parameters, along with treatment and insecticide policies, hold promise as effective control measures in mitigating the spread and impact of dengue infection.

Keywords: Fractional Dynamics; Infectious Disease; Nonlinear Equations; Resistance to Drug; Numerical Scheme; Dynamical Behavior (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401085

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