This work proposes a novel and comprehensive fractional-order model for the transmission dynamics and optimal control of a zoonotic avian–human influenza system involving two viral strains. The model distinguishes itself from classical approaches in three key aspects: (i) the use of Caputo fractional derivatives to incorporate memory effects and long-term temporal correlations in biological processes; (ii) the inclusion of three epidemiologically distinct compartments— humans, poultry, and a contaminated environment—each contributing to disease propagation; and (iii) the integration of nonlinear behavioral (awareness-driven) responses that modify transmission rates based on perceived infection risk. Six time-dependent control measures are embedded: vaccination, treatment for both human strains, culling of infected birds, environmental decontamination, and public awareness campaigns. An optimal control framework is formulated via a cost functional that jointly minimizes the health and economic burdens. Pontryagin’s maximum principle is used to derive the necessary optimal conditions, and the resulting system is solved using the forward–backward sweep method with L1 discretization. Simulation results reveal that the fractional order <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> substantially alters the epidemic curve and the cost-efficiency of interventions. Notably, the combined strategy <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\{u_1, u_2, u_6\}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">{</mo> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>u</mi> <mn>6</mn> </msub> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>—which simultaneously targets pharmaceutical and behavioral fronts—emerges as the most effective for reducing human infections, while <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\{u_4, u_5\}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">{</mo> <msub> <mi>u</mi> <mn>4</mn> </msub> <mo>,</mo> <msub> <mi>u</mi> <mn>5</mn> </msub> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation> proves crucial in mitigating environmental and avian sources. These findings underscore the value of fractional modeling for capturing complex, memory-dependent transmission mechanisms and inform the design of robust public health policies for managing zoonotic diseases.

Fractional optimal control of avian–human influenza with environmental and behavioral interactions

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发表日期：

2026年2月28日

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Asiyeh Ebrahimzadeh

摘要

This work proposes a novel and comprehensive fractional-order model for the transmission dynamics and optimal control of a zoonotic avian–human influenza system involving two viral strains. The model distinguishes itself from classical approaches in three key aspects: (i) the use of Caputo fractional derivatives to incorporate memory effects and long-term temporal correlations in biological processes; (ii) the inclusion of three epidemiologically distinct compartments— humans, poultry, and a contaminated environment—each contributing to disease propagation; and (iii) the integration of nonlinear behavioral (awareness-driven) responses that modify transmission rates based on perceived infection risk. Six time-dependent control measures are embedded: vaccination, treatment for both human strains, culling of infected birds, environmental decontamination, and public awareness campaigns. An optimal control framework is formulated via a cost functional that jointly minimizes the health and economic burdens. Pontryagin’s maximum principle is used to derive the necessary optimal conditions, and the resulting system is solved using the forward–backward sweep method with L1 discretization. Simulation results reveal that the fractional order $\alpha $ $α$ substantially alters the epidemic curve and the cost-efficiency of interventions. Notably, the combined strategy $\{u_1, u_2, u_6\}$ ${u_{1}, u_{2}, u_{6}}$ —which simultaneously targets pharmaceutical and behavioral fronts—emerges as the most effective for reducing human infections, while $\{u_4, u_5\}$ ${u_{4}, u_{5}}$ proves crucial in mitigating environmental and avian sources. These findings underscore the value of fractional modeling for capturing complex, memory-dependent transmission mechanisms and inform the design of robust public health policies for managing zoonotic diseases.