This study develops a fractional-order model of Chlamydia trachomatis transmission that incorporates memory effects and evaluates four key control measures-mass awareness, vaccination, treatment, and environmental hygiene-operating through direct and indirect infection pathways. The model extends conventional epidemiological frameworks by integrating an environmental compartment to track bacterial concentration alongside six human compartments (susceptible, vaccinated, exposed, asymptomatic infected, symptomatic infected, and recovered). We prove the existence and uniqueness of solutions and demonstrate Ulam–Hyers stability, ensuring that minor perturbations in initial conditions lead to only minimal deviations in long-term dynamics. The basic reproduction number, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2425_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$R_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>, is derived using the next-generation matrix approach. Numerical simulations reveal that the disease-free equilibrium is unstable when <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2425_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <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>, suggesting that even minimal disease introduction can lead to an outbreak. Conversely, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2425_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <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> indicates the potential for endemic persistence. Furthermore, increased memory effects result in fewer symptomatic and recovered individuals, suggesting that individuals with prior infections can better implement preventive measures. Our findings indicate that integrating fractional-order modelling with targeted public health interventions can substantially mitigate Chlamydia transmission, enhancing epidemiological predictions and informing effective disease control strategies.

Modeling Chlamydia transmission with caputo fractional derivatives: exploring memory effects and control strategies

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发表日期：

2025年6月23日

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Nkuba Nyerere,
Stephen Edward

摘要

This study develops a fractional-order model of Chlamydia trachomatis transmission that incorporates memory effects and evaluates four key control measures-mass awareness, vaccination, treatment, and environmental hygiene-operating through direct and indirect infection pathways. The model extends conventional epidemiological frameworks by integrating an environmental compartment to track bacterial concentration alongside six human compartments (susceptible, vaccinated, exposed, asymptomatic infected, symptomatic infected, and recovered). We prove the existence and uniqueness of solutions and demonstrate Ulam–Hyers stability, ensuring that minor perturbations in initial conditions lead to only minimal deviations in long-term dynamics. The basic reproduction number, $R_0$ $R_{0}$ , is derived using the next-generation matrix approach. Numerical simulations reveal that the disease-free equilibrium is unstable when $R_0 < 1$ $R_{0} < 1$ , suggesting that even minimal disease introduction can lead to an outbreak. Conversely, $R_0 > 1$ $R_{0} > 1$ indicates the potential for endemic persistence. Furthermore, increased memory effects result in fewer symptomatic and recovered individuals, suggesting that individuals with prior infections can better implement preventive measures. Our findings indicate that integrating fractional-order modelling with targeted public health interventions can substantially mitigate Chlamydia transmission, enhancing epidemiological predictions and informing effective disease control strategies.