Stochastic Dynamics of Urban Predator-Prey Systems: Integrating Human Disturbance and Functional Responses

Ogethakpo Arhonefe Joseph; Ogoegbulem Ozioma; Apanapudor Sarduana Joshua; Helen Onovwerosuoke Sanubi

doi:doi:10.11648/j.ajam.20251304.15

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Stochastic Dynamics of Urban Predator-Prey Systems: Integrating Human Disturbance and Functional Responses

Ogethakpo Arhonefe Joseph^*

, Ogoegbulem Ozioma

, Apanapudor Sarduana Joshua

, Helen Onovwerosuoke Sanubi

Published in American Journal of Applied Mathematics (Volume 13, Issue 4)

Received: 10 July 2025 Accepted: 28 July 2025 Published: 20 August 2025

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Abstract

Urban ecosystems exhibit complex predator-prey dynamics increasingly disrupted by anthropogenic disturbances (e.g., noise, habitat fragmentation). Classical Lotka-Volterra (LV) models fail to capture these human-induced stressors, and integrated frameworks incorporating functional responses, stochasticity, and spatial dynamics remain scarce. We develop a comprehensive stochastic model to quantify how human disturbance reshapes predator-prey interactions in urban landscapes, using rat-cat systems as a case study. Our framework extends the LV model to incorporate: (i) human disturbance as an external mortality factor, (ii) Holling Type III functional responses to model predation saturation and prey refugia, (iii) multiplicative noise and periodic forcing to capture stochastic disturbance regimes, and (iv) spatial diffusion across fragmented habitats. We non-dimensionalize the system to generalize dynamics and analyze stability, bifurcations, and noise-induced transitions. Numerical simulations (MATLAB) reveal three key outcomes: (1) Human disturbance disrupts classical oscillations, inducing quasi-periodic cycles and elevating extinction risks; (2) Stochasticity lowers collapse thresholds by 25% compared to deterministic predictions; (3) Spatial diffusion drives pattern formation (e.g., disturbance shadows, prey hotspots) through habitat coupling. Results highlight the extreme vulnerability of urban wildlife to anthropogenic pressures, demonstrating how disturbance intensity (μ) governs system stability (μ>0.7 triggers irreversible collapse). The model provides a predictive framework for conservation strategies, emphasizing refuge enhancement (ϕ>0.005) and phased interventions synchronized with population cycles.

Published in	American Journal of Applied Mathematics (Volume 13, Issue 4)
DOI	10.11648/j.ajam.20251304.15
Page(s)	282-291
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Urban Predator-prey Systems, Stochastic Dynamics, Human Disturbance, Holling Type III Functional Response, Stability Thresholds, Spatial Diffusion

References

[1]	Alebraheem, J. (2025). Asymptotic stability of deterministic and stochastic prey-predator models with prey herd immigration [J]. AIMS Mathematics, 10(3): 4620-4640. https://doi.org/10.3934/math.2025214
[2]	Barceló, G., Donadio, E., Alldredge, M. W., & Pauli, J. N. (2025). Human disturbance alters the foraging and spatiotemporal activity of a large carnivore. Oecologia, 207(7), 112. https://doi.org/10.1007/s00442-025-05752-x
[3]	Berestycki, H., & Zilio, A. (2019). Predator-Prey Models with Competition: The Emergence of Territoriality. The American naturalist, 193(3), 436-446. https://doi.org/10.1086/701670
[4]	Danane, J., Yavuz, M., & Yıldız, M. (2023). Stochastic Modeling of Three-Species Prey-Predator Model Driven by Lévy Jump with Mixed Holling-II and Beddington-DeAngelis Functional Responses. Fractal and Fractional, 7(10), 751. https://doi.org/10.3390/fractalfract710075
[5]	Dawes, J. H. P. & Souza, M. O. (2013). A derivation of Holling's type I, II and III functional responses in predator-prey systems, Journal of Theoretical Biology, Volume 327, P 11-22, ISSN 0022-5193, https://doi.org/10.1016/j.jtbi.2013.02.017
[6]	Fraterrigo, J. M. & Rusak, J. A. (2008). Disturbance-driven changes in the variability of ecological patterns and processes. Ecology Letters, 11: 756-770, https://doi.org/10.1111/j.1461-0248.2008.01191.x
[7]	Gorczynski, D., Hsieh, C., Luciano, J. T., Ahumada, J., Espinosa, S., Johnson, S., Rovero, F., Santos, F., Andrianarisoa, M. H., Astaiza, J. H., Jansen, P. A., Kayijamahe, C., Lima, M. G. M., Salvador, J., & Beaudrot, L. (2021). Tropical mammal functional diversity increases with productivity but decreases with anthropogenic disturbance. Proceedings: Biological Sciences, 288(1945), 1-8. https://www.jstor.org/stable/27014404
[8]	Gough, C. M., Buma, B., Jentsch, A., Mathes, K. C., & Fahey, R. T. (2024). Disturbance theory for ecosystem ecologists: A primer. Ecology and Evolution, 14, e11403. https://doi.org/10.1002/ece3.11403
[9]	Hanski, I. (1998). Metapopulation dynamics. Nature, 396, 41-49. https://doi.org/10.1038/23876
[10]	Holling, C. S. (2012). The components of predation. The Canadian Entomologist, 91(5), 293-320. https://doi.org/10.4039/Ent91293-5
[11]	LaBarge, L. R., Krofel, M., Allen, M. L., Hill, R. A., Welch, A. J., Allan, A. T. L. (2024). Keystone individuals-linking predator traits to community ecology, Trends in Ecology & Evolution, 39(11), 983-994, ISSN 0169-5347, https://doi.org/10.1016/j.tree.2024.07.001
[12]	Li, X., Hu, W., Bleisch, W. V., Li, Q., Wang, H., Lu, W., Sun, J., Zhang, F., Ti, Bu, & Jiang, X. (2022). Functional diversity loss and change in nocturnal behavior of mammals under anthropogenic disturbance. Conservation Biology, 36, e13839. https://doi.org/10.1111/cobi.13839
[13]	Liu, M., Deng, M., Ji, W. (2025). Dynamics of a stochastic predator-prey model with fear effect and Beddington-DeAngelis functional response. Discrete and Continuous Dynamical Systems - B, 30(8): 3084-3103. https://doi.org/10.3934/dcdsb.2025009
[14]	Ogethakpo, A. J., & Ojobor, S. A. (2021). The Lotka-Volterra Predator-Prey Model with Disturbance. Nigerian Journal of Science and Environment, Vol. 19(2) 135-144.
[15]	Olayemi, A., Cadar, D., Magassouba, N., Obadare, A., Kourouma, F., Oyeyiola, A., Fasogbon, S., Igbokwe, J., Rieger, T., Bockholt, S., Jérôme, H., Schmidt-Chanasit, J., Garigliany, M., Lorenzen, S., Igbahenah, F., Fichet, J. N., Ortsega, D., Omilabu, S., Günther, S., & Fichet-Calvet, E. (2016). New Hosts of The Lassa Virus. Scientific reports, 6, 25280. https://doi.org/10.1038/srep25280
[16]	Palamara, G. M., Capitán, J. A., & Alonso, D. (2021). The Stochastic Nature of Functional Responses. Entropy, 23(5), 575. https://doi.org/10.3390/e23050575
[17]	Penteriani, V., Kuparinen, A., del Mar Delgado, M., Palomares, F., López-Bao, J. V., Fedriani, J. M., Calzada, J., Moreno, S., Villafuerte, R., Campioni, L., & Lourenço, R. (2013). Responses of a top and a meso predator and their prey to moon phases. Oecologia, 173(3), 753-766. https://doi.org/10.1007/s00442-013-2651-6
[18]	Schneider, M. F. (2001). Habitat Loss, Fragmentation and Predator Impact: Spatial Implications for Prey Conservation. Journal of Applied Ecology, 38(4), 720-735. http://www.jstor.org/stable/827314
[19]	Shao, Y. (2022). Dynamics and optimal harvesting of a stochastic predator-prey system with regime switching, S-type distributed time delays and Lévy jumps [J]. AIMS Mathematics, 7(3): 4068-4093. https://doi.org/10.3934/math.2022225
[20]	Sturtevant, B. R., & Fortin, M. (2021). Understanding and Modeling Forest Disturbance Interactions at the Landscape Level. Frontiers in Ecology and Evolution. https://doi.org/10.3389/fevo.2021.653647
[21]	Ton, T. V. & Yagi, A. (2011). "Dynamics of a stochastic predator-prey model with the Beddington-DeAngelis functional response," Communications on Stochastic Analysis: Vol. 5: No. 2, Article 8. https://doi.org/10.31390/cosa.5.2.08
[22]	Wang, W., Zhang, L., Xue, Y., Jin, Z. (2008). “Spatiotemporal Pattern Formation of Beddington-DeAngelis-Type Predator-Prey Model,” arXiv: 0801.0797v1 [q-bio.PE], https://doi.org/10.48550/arXiv.0801.0797
[23]	Wang, X., & Zhang, T. (2022). Dynamics of Random Predation Model with Fear Effect and Avoidance Sensitivity [J]. Theoretical Mathematics, 12(9): 1399-1410. https://doi.org/10.12677/PM.2022.129153
[24]	Xu, C., Lu, C., Li, Y. (2024). Dynamical bifurcation of a stochastic Holling-II predator-prey model with infinite distributed delays, Communications in Nonlinear Science and Numerical Simulation, Volume 135, 108077, ISSN 1007-5704, https://doi.org/10.1016/j.cnsns.2024.108077

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APA Style

Joseph, O. A., Ozioma, O., Joshua, A. S., Sanubi, H. O. (2025). Stochastic Dynamics of Urban Predator-Prey Systems: Integrating Human Disturbance and Functional Responses. American Journal of Applied Mathematics, 13(4), 282-291. https://doi.org/10.11648/j.ajam.20251304.15

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ACS Style

Joseph, O. A.; Ozioma, O.; Joshua, A. S.; Sanubi, H. O. Stochastic Dynamics of Urban Predator-Prey Systems: Integrating Human Disturbance and Functional Responses. Am. J. Appl. Math. 2025, 13(4), 282-291. doi: 10.11648/j.ajam.20251304.15

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AMA Style

Joseph OA, Ozioma O, Joshua AS, Sanubi HO. Stochastic Dynamics of Urban Predator-Prey Systems: Integrating Human Disturbance and Functional Responses. Am J Appl Math. 2025;13(4):282-291. doi: 10.11648/j.ajam.20251304.15

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@article{10.11648/j.ajam.20251304.15,
  author = {Ogethakpo Arhonefe Joseph and Ogoegbulem Ozioma and Apanapudor Sarduana Joshua and Helen Onovwerosuoke Sanubi},
  title = {Stochastic Dynamics of Urban Predator-Prey Systems: Integrating Human Disturbance and Functional Responses
},
  journal = {American Journal of Applied Mathematics},
  volume = {13},
  number = {4},
  pages = {282-291},
  doi = {10.11648/j.ajam.20251304.15},
  url = {https://doi.org/10.11648/j.ajam.20251304.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20251304.15},
  abstract = {Urban ecosystems exhibit complex predator-prey dynamics increasingly disrupted by anthropogenic disturbances (e.g., noise, habitat fragmentation). Classical Lotka-Volterra (LV) models fail to capture these human-induced stressors, and integrated frameworks incorporating functional responses, stochasticity, and spatial dynamics remain scarce. We develop a comprehensive stochastic model to quantify how human disturbance reshapes predator-prey interactions in urban landscapes, using rat-cat systems as a case study. Our framework extends the LV model to incorporate: (i) human disturbance as an external mortality factor, (ii) Holling Type III functional responses to model predation saturation and prey refugia, (iii) multiplicative noise and periodic forcing to capture stochastic disturbance regimes, and (iv) spatial diffusion across fragmented habitats. We non-dimensionalize the system to generalize dynamics and analyze stability, bifurcations, and noise-induced transitions. Numerical simulations (MATLAB) reveal three key outcomes: (1) Human disturbance disrupts classical oscillations, inducing quasi-periodic cycles and elevating extinction risks; (2) Stochasticity lowers collapse thresholds by 25% compared to deterministic predictions; (3) Spatial diffusion drives pattern formation (e.g., disturbance shadows, prey hotspots) through habitat coupling. Results highlight the extreme vulnerability of urban wildlife to anthropogenic pressures, demonstrating how disturbance intensity (μ) governs system stability (μ>0.7 triggers irreversible collapse). The model provides a predictive framework for conservation strategies, emphasizing refuge enhancement (ϕ>0.005) and phased interventions synchronized with population cycles.},
 year = {2025}
}

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TY  - JOUR
T1  - Stochastic Dynamics of Urban Predator-Prey Systems: Integrating Human Disturbance and Functional Responses

AU  - Ogethakpo Arhonefe Joseph
AU  - Ogoegbulem Ozioma
AU  - Apanapudor Sarduana Joshua
AU  - Helen Onovwerosuoke Sanubi
Y1  - 2025/08/20
PY  - 2025
N1  - https://doi.org/10.11648/j.ajam.20251304.15
DO  - 10.11648/j.ajam.20251304.15
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 282
EP  - 291
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20251304.15
AB  - Urban ecosystems exhibit complex predator-prey dynamics increasingly disrupted by anthropogenic disturbances (e.g., noise, habitat fragmentation). Classical Lotka-Volterra (LV) models fail to capture these human-induced stressors, and integrated frameworks incorporating functional responses, stochasticity, and spatial dynamics remain scarce. We develop a comprehensive stochastic model to quantify how human disturbance reshapes predator-prey interactions in urban landscapes, using rat-cat systems as a case study. Our framework extends the LV model to incorporate: (i) human disturbance as an external mortality factor, (ii) Holling Type III functional responses to model predation saturation and prey refugia, (iii) multiplicative noise and periodic forcing to capture stochastic disturbance regimes, and (iv) spatial diffusion across fragmented habitats. We non-dimensionalize the system to generalize dynamics and analyze stability, bifurcations, and noise-induced transitions. Numerical simulations (MATLAB) reveal three key outcomes: (1) Human disturbance disrupts classical oscillations, inducing quasi-periodic cycles and elevating extinction risks; (2) Stochasticity lowers collapse thresholds by 25% compared to deterministic predictions; (3) Spatial diffusion drives pattern formation (e.g., disturbance shadows, prey hotspots) through habitat coupling. Results highlight the extreme vulnerability of urban wildlife to anthropogenic pressures, demonstrating how disturbance intensity (μ) governs system stability (μ>0.7 triggers irreversible collapse). The model provides a predictive framework for conservation strategies, emphasizing refuge enhancement (ϕ>0.005) and phased interventions synchronized with population cycles.
VL  - 13
IS  - 4
ER  -

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Author Information

Ogethakpo Arhonefe Joseph

Department of Mathematics, Delta State University, Abraka, Nigeria

Contact Email

http://orcid.org/0009-0004-6013-1341
Ogoegbulem Ozioma

Department of Mathematics, Dennis Osadebay University, Asaba, Nigeria

Contact Email

http://orcid.org/0009-0002-0547-032X
Apanapudor Sarduana Joshua

Department of Mathematics, Delta State University, Abraka, Nigeria

Contact Email

http://orcid.org/0000-0001-9567-1154
Helen Onovwerosuoke Sanubi

Department of Mathematics and Computer Science, Delta State College of Education, Mosogar, Nigeria

Contact Email

http://orcid.org/0009-0009-8241-8761

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APA Style

Joseph, O. A., Ozioma, O., Joshua, A. S., Sanubi, H. O. (2025). Stochastic Dynamics of Urban Predator-Prey Systems: Integrating Human Disturbance and Functional Responses. American Journal of Applied Mathematics, 13(4), 282-291. https://doi.org/10.11648/j.ajam.20251304.15

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ACS Style

Joseph, O. A.; Ozioma, O.; Joshua, A. S.; Sanubi, H. O. Stochastic Dynamics of Urban Predator-Prey Systems: Integrating Human Disturbance and Functional Responses. Am. J. Appl. Math. 2025, 13(4), 282-291. doi: 10.11648/j.ajam.20251304.15

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AMA Style

Joseph OA, Ozioma O, Joshua AS, Sanubi HO. Stochastic Dynamics of Urban Predator-Prey Systems: Integrating Human Disturbance and Functional Responses. Am J Appl Math. 2025;13(4):282-291. doi: 10.11648/j.ajam.20251304.15

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@article{10.11648/j.ajam.20251304.15,
  author = {Ogethakpo Arhonefe Joseph and Ogoegbulem Ozioma and Apanapudor Sarduana Joshua and Helen Onovwerosuoke Sanubi},
  title = {Stochastic Dynamics of Urban Predator-Prey Systems: Integrating Human Disturbance and Functional Responses
},
  journal = {American Journal of Applied Mathematics},
  volume = {13},
  number = {4},
  pages = {282-291},
  doi = {10.11648/j.ajam.20251304.15},
  url = {https://doi.org/10.11648/j.ajam.20251304.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20251304.15},
  abstract = {Urban ecosystems exhibit complex predator-prey dynamics increasingly disrupted by anthropogenic disturbances (e.g., noise, habitat fragmentation). Classical Lotka-Volterra (LV) models fail to capture these human-induced stressors, and integrated frameworks incorporating functional responses, stochasticity, and spatial dynamics remain scarce. We develop a comprehensive stochastic model to quantify how human disturbance reshapes predator-prey interactions in urban landscapes, using rat-cat systems as a case study. Our framework extends the LV model to incorporate: (i) human disturbance as an external mortality factor, (ii) Holling Type III functional responses to model predation saturation and prey refugia, (iii) multiplicative noise and periodic forcing to capture stochastic disturbance regimes, and (iv) spatial diffusion across fragmented habitats. We non-dimensionalize the system to generalize dynamics and analyze stability, bifurcations, and noise-induced transitions. Numerical simulations (MATLAB) reveal three key outcomes: (1) Human disturbance disrupts classical oscillations, inducing quasi-periodic cycles and elevating extinction risks; (2) Stochasticity lowers collapse thresholds by 25% compared to deterministic predictions; (3) Spatial diffusion drives pattern formation (e.g., disturbance shadows, prey hotspots) through habitat coupling. Results highlight the extreme vulnerability of urban wildlife to anthropogenic pressures, demonstrating how disturbance intensity (μ) governs system stability (μ>0.7 triggers irreversible collapse). The model provides a predictive framework for conservation strategies, emphasizing refuge enhancement (ϕ>0.005) and phased interventions synchronized with population cycles.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Stochastic Dynamics of Urban Predator-Prey Systems: Integrating Human Disturbance and Functional Responses

AU  - Ogethakpo Arhonefe Joseph
AU  - Ogoegbulem Ozioma
AU  - Apanapudor Sarduana Joshua
AU  - Helen Onovwerosuoke Sanubi
Y1  - 2025/08/20
PY  - 2025
N1  - https://doi.org/10.11648/j.ajam.20251304.15
DO  - 10.11648/j.ajam.20251304.15
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 282
EP  - 291
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20251304.15
AB  - Urban ecosystems exhibit complex predator-prey dynamics increasingly disrupted by anthropogenic disturbances (e.g., noise, habitat fragmentation). Classical Lotka-Volterra (LV) models fail to capture these human-induced stressors, and integrated frameworks incorporating functional responses, stochasticity, and spatial dynamics remain scarce. We develop a comprehensive stochastic model to quantify how human disturbance reshapes predator-prey interactions in urban landscapes, using rat-cat systems as a case study. Our framework extends the LV model to incorporate: (i) human disturbance as an external mortality factor, (ii) Holling Type III functional responses to model predation saturation and prey refugia, (iii) multiplicative noise and periodic forcing to capture stochastic disturbance regimes, and (iv) spatial diffusion across fragmented habitats. We non-dimensionalize the system to generalize dynamics and analyze stability, bifurcations, and noise-induced transitions. Numerical simulations (MATLAB) reveal three key outcomes: (1) Human disturbance disrupts classical oscillations, inducing quasi-periodic cycles and elevating extinction risks; (2) Stochasticity lowers collapse thresholds by 25% compared to deterministic predictions; (3) Spatial diffusion drives pattern formation (e.g., disturbance shadows, prey hotspots) through habitat coupling. Results highlight the extreme vulnerability of urban wildlife to anthropogenic pressures, demonstrating how disturbance intensity (μ) governs system stability (μ>0.7 triggers irreversible collapse). The model provides a predictive framework for conservation strategies, emphasizing refuge enhancement (ϕ>0.005) and phased interventions synchronized with population cycles.
VL  - 13
IS  - 4
ER  -

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