<p>Dengue is a resurging ailment infecting an estimated 100–140 million individuals annually. To understand the transmission mechanism of dengue, we define a nine-compartmental (six compartments for humans and three compartments for vectors) model incorporating fractional-order derivatives. Three different control measures, namely insecticide control for mosquitoes, treatment, and public awareness campaigns for the human population, are considered for the mathematical model to be proposed. We assess the existence and uniqueness of the solution and calculate the basic reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$(R_0)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> using the next-generation matrix approach. It has been established that the proposed system has two equilibria viz: disease-free and endemic equilibrium, depending on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$R_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>. The stability of these equilibria has been investigated, considering <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$R_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> as the threshold parameter. Also, we have found that at <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$R_0 = 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, the system produces a transcritical bifurcation. Through numerical simulation with feasible parameter values, we demonstrate that employing controls decreases the infection, and all controls lead to a quicker removal of the disease. A cost-effectiveness analysis has been performed utilizing infection averted ratio (IAR) and incremental cost-effectiveness ratio (ICER) methods to determine the most cost-effective policy. Finally, the model has been calibrated using real dengue cases in Cambodia, one of the most dengue-prone countries, resulting in short-term predictions showing that the fractional-order system is more appropriate.</p>

COMPLEX DYNAMICS OF A HOST-VECTOR DYNAMICS OF DENGUE INFECTION INCORPORATING OPTIMAL CONTROL STRATEGY WITH COST-EFFECTIVENESS: A FRACTIONAL-ORDER DERIVATIVE METHOD

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发表日期：

2025年3月17日

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Sathi Patra,
Soovoojeet Jana,
Sayani Adak,
Suvankar Majee,
T. K. Kar

摘要

Dengue is a resurging ailment infecting an estimated 100–140 million individuals annually. To understand the transmission mechanism of dengue, we define a nine-compartmental (six compartments for humans and three compartments for vectors) model incorporating fractional-order derivatives. Three different control measures, namely insecticide control for mosquitoes, treatment, and public awareness campaigns for the human population, are considered for the mathematical model to be proposed. We assess the existence and uniqueness of the solution and calculate the basic reproduction number $(R_0)$ $(R_{0})$ using the next-generation matrix approach. It has been established that the proposed system has two equilibria viz: disease-free and endemic equilibrium, depending on $R_0$ $R_{0}$ . The stability of these equilibria has been investigated, considering $R_0$ $R_{0}$ as the threshold parameter. Also, we have found that at $R_0 = 1$ $R_{0} = 1$ , the system produces a transcritical bifurcation. Through numerical simulation with feasible parameter values, we demonstrate that employing controls decreases the infection, and all controls lead to a quicker removal of the disease. A cost-effectiveness analysis has been performed utilizing infection averted ratio (IAR) and incremental cost-effectiveness ratio (ICER) methods to determine the most cost-effective policy. Finally, the model has been calibrated using real dengue cases in Cambodia, one of the most dengue-prone countries, resulting in short-term predictions showing that the fractional-order system is more appropriate.