<p>Fowlpox is a highly contagious viral disease that primarily affects chickens and turkeys, though it can infect various bird species. The disease spreads rapidly through vectors, contaminated environments, and infected hosts, and is challenging to control due to seasonal variations influencing its dynamics. In this study, a deterministic model incorporating periodic mosquito growth and virus decay rates is formulated and analysed to assess the impact of seasonality in the disease dynamics. The model is further modified by incorporating time-dependent control parameters and analysed to evaluate the effect of insecticide spraying and environmental decontamination on the disease management. Optimal control theory is applied to determine the effectiveness of these interventions. The basic reproduction number, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2292_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$\Re _{0}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℜ</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>, is computed using the time-averaging method and the linear operator approach, and the results are analysed. The trajectories derived from the time-averaging method alternately overestimate and underestimate the disease risk as the amplitude of seasonal oscillations increases. In contrast, the linear operator approach consistently shows that <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2292_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">$\Re _{0}<1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>ℜ</mi> <mn>0</mn> </msub> <mo><</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> regardless of the virus decay rate. Optimal results demonstrated that environmental decontamination is more effective than the insecticide spraying though relying on one strategy does not completely eliminate fowl pox disease in the chicken. However, combining both control measures yields significantly better outcomes.</p>

Seasonal dynamics and optimal control analysis of fowlpox disease

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发表日期：

2025年2月4日

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Cosmas Muhumuza,
Joseph Y. T. Mugisha,
Fred Mayambala,
John Kitayimbwa

摘要

Fowlpox is a highly contagious viral disease that primarily affects chickens and turkeys, though it can infect various bird species. The disease spreads rapidly through vectors, contaminated environments, and infected hosts, and is challenging to control due to seasonal variations influencing its dynamics. In this study, a deterministic model incorporating periodic mosquito growth and virus decay rates is formulated and analysed to assess the impact of seasonality in the disease dynamics. The model is further modified by incorporating time-dependent control parameters and analysed to evaluate the effect of insecticide spraying and environmental decontamination on the disease management. Optimal control theory is applied to determine the effectiveness of these interventions. The basic reproduction number, $\Re _{0}$ $ℜ_{0}$ , is computed using the time-averaging method and the linear operator approach, and the results are analysed. The trajectories derived from the time-averaging method alternately overestimate and underestimate the disease risk as the amplitude of seasonal oscillations increases. In contrast, the linear operator approach consistently shows that $\Re _{0}<1$ $ℜ_{0} < 1$ regardless of the virus decay rate. Optimal results demonstrated that environmental decontamination is more effective than the insecticide spraying though relying on one strategy does not completely eliminate fowl pox disease in the chicken. However, combining both control measures yields significantly better outcomes.