{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T05:15:20Z","timestamp":1762924520298,"version":"3.45.0"},"reference-count":36,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T00:00:00Z","timestamp":1762041600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This study developed an eco-epidemiological model of a prey\u2013predator system with three populations\u2014susceptible prey, infected prey, and predator\u2014to model the transmission of disease and contact epidemiology based on direct interactions between susceptible and infected prey. For the predictive modeling to be relevant, we developed a system and performed stability analysis at global and local scales to assess species persistence or extinction. We conducted bifurcation analysis to identify the optimal values of important parameters in which small modifications produced noticeable changes in the population dynamics. Under varying ecological and epidemiological elements, the simulation findings revealed population stability. Based on its effect on species survival and food chain dynamics, our results shed light on the function of cooperative hunting in preserving ecological equilibrium. We discuss how ecosystems are formed by disease and predator\u2013prey interactions, offering data for wildlife management and conservation.<\/jats:p>","DOI":"10.3390\/computation13110254","type":"journal-article","created":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T13:55:22Z","timestamp":1762178122000},"page":"254","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Modeling Disease Dynamics in a Prey\u2013Predator System with Competition, Fear, and Cooperative Hunting"],"prefix":"10.3390","volume":"13","author":[{"given":"Alyaa Hussain","family":"Naser","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, University of Baghdad, Baghdad 10071, Iraq"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1935-0620","authenticated-orcid":false,"given":"Dahlia Khaled","family":"Bahlool","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Baghdad, Baghdad 10071, Iraq"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,2]]},"reference":[{"unstructured":"Kapur, J.N. (1988). Mathematical Modelling, John Wiley & Sons.","key":"ref_1"},{"unstructured":"Farkas, M. (2001). Dynamical Models in Biology, Academic Press.","key":"ref_2"},{"doi-asserted-by":"crossref","unstructured":"Haefner, J.W. (2005). Modeling Biological Systems: Principles and Applications, Springer. [2nd ed.].","key":"ref_3","DOI":"10.1007\/b106568"},{"doi-asserted-by":"crossref","unstructured":"Teschl, G. (2012). Ordinary Differential Equations and Dynamical Systems, American Mathematical Society.","key":"ref_4","DOI":"10.1090\/gsm\/140"},{"doi-asserted-by":"crossref","unstructured":"Fishwick, P.A. (2007). Handbook of Dynamic System Modeling, Chapman and Hall\/CRC.","key":"ref_5","DOI":"10.1201\/9781420010855.pt1"},{"unstructured":"Gershenfeld, N. (1999). The Nature of Mathematical Modeling, Cambridge University Press.","key":"ref_6"},{"doi-asserted-by":"crossref","unstructured":"Zhang, H., Yuan, X., Zou, H., Zhao, L., Wang, Z., Guo, F., and Liu, Z. (2024). The Spatiotemporal Dynamics of Insect Predator\u2013Prey System Incorporating Refuge Effect. Entropy, 26.","key":"ref_7","DOI":"10.3390\/e26030196"},{"doi-asserted-by":"crossref","unstructured":"Choh, Y., Sabelis, M.W., and Janssen, A. (2017). Predatory interactions between prey affect patch selection by predators. Behav. Ecol. Sociobiol., 71.","key":"ref_8","DOI":"10.1007\/s00265-017-2288-2"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2014","DOI":"10.24996\/ijs.2025.66.5.20","article-title":"Modeling and analysis of a prey\u2013predator\u2013scavenger system encompassing fear, hunting cooperation, and harvesting","volume":"66","author":"Ibrahim","year":"2025","journal-title":"Iraqi J. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2455","DOI":"10.24996\/ijs.2025.66.6.22","article-title":"The influence of fear and predator-dependent refuge on the dynamics of a harvested prey\u2013predator model with disease in predator","volume":"66","author":"Abdullah","year":"2025","journal-title":"Iraqi J. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"100705","DOI":"10.1016\/j.padiff.2024.100705","article-title":"Improving the hepatitis viral transmission model\u2019s dynamics by vaccination and contrasting it with the fractional-order model","volume":"10","author":"Yaseen","year":"2024","journal-title":"Partial Differ. Equ. Appl. Math."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3904","DOI":"10.1073\/pnas.071061998","article-title":"The contribution of trait-mediated indirect effects to the net effects of a predator","volume":"98","author":"Peacor","year":"2001","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4314\/ijest.v6i2.1","article-title":"Influence of prey reserve in two preys and one predator system","volume":"6","author":"Agarwal","year":"2014","journal-title":"Int. J. Eng. Sci. Technol."},{"key":"ref_14","first-page":"201","article-title":"Stochastic and delay analysis of two preys and one predator ecological system with competition among preys and self interaction","volume":"2","author":"Anitha","year":"2018","journal-title":"Dyn. Syst. Applions."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1080\/13873950600682580","article-title":"Role of transmissible disease in an infected prey-dependent predator\u2013prey system","volume":"13","author":"Haque","year":"2007","journal-title":"Math. Comput. Model. Dyn. Syst."},{"doi-asserted-by":"crossref","unstructured":"Venturino, E. (2022). Disease Spread among Hunted and Retaliating Herding Prey. Mathematics, 10.","key":"ref_16","DOI":"10.3390\/math10234397"},{"unstructured":"Al-Husseiny, H.F., Ali, N.F., and Mohsen, A.A. (2021). The effect of epidemic disease outbreaks on the dynamic behavior of a prey\u2013predator model with Holling type II functional response. Commun. Math. Biol. Neurosci., 2021.","key":"ref_17"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3285","DOI":"10.1007\/s11071-020-05490-0","article-title":"Global dynamics of a Holling type-III two-prey\u2013one-predator discrete model with optimal harvest strategy","volume":"99","author":"Banerjee","year":"2020","journal-title":"Nonlinear Dyn."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1725","DOI":"10.1016\/j.na.2005.11.049","article-title":"Influence of prey reserve in a prey\u2013predator fishery","volume":"65","author":"Kar","year":"2006","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"02008","DOI":"10.1051\/matecconf\/202237202008","article-title":"Dynamics twin cannibalism of two predator and two prey system with prey defense","volume":"372","author":"Pratama","year":"2022","journal-title":"MATEC Web Conf."},{"doi-asserted-by":"crossref","unstructured":"Liu, J., Hu, J., Yuen, P., and Li, F. (2022). A Seasonally Competitive M-Prey and N-Predator Impulsive System Modeled by General Functional Response for Integrated Pest Management. Mathematics, 10.","key":"ref_21","DOI":"10.3390\/math10152687"},{"doi-asserted-by":"crossref","unstructured":"Peng, C., and Jiang, J. (2025). Dynamical Regimes in a Delayed Predator\u2013Prey Model with Predator Hunting Cooperation: Bifurcations, Stability, and Complex Dynamics. Modelling, 6.","key":"ref_22","DOI":"10.3390\/modelling6030084"},{"doi-asserted-by":"crossref","unstructured":"Berardo, C., Bulai, I.M., and Venturino, E. (2021). Interactions Obtained from Basic Mechanistic Principles: Prey Herds and Predators. Mathematics, 9.","key":"ref_23","DOI":"10.3390\/math9202555"},{"key":"ref_24","first-page":"144","article-title":"An ecoepidemic model with diseased predators and prey group defense","volume":"34","author":"Belvisi","year":"2013","journal-title":"Math. Biosci. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"642","DOI":"10.1016\/j.crvi.2009.02.002","article-title":"Stability and bifurcation of a prey-predator model with time delay","volume":"332","author":"Kar","year":"2009","journal-title":"C. R. Biol."},{"key":"ref_26","first-page":"1","article-title":"Predator\u2013prey system with the effect of environmental fluctuation","volume":"30","author":"Lan","year":"2014","journal-title":"VNU J. Sci. Math. Phys."},{"doi-asserted-by":"crossref","unstructured":"Alebraheem, J. (2021). Dynamics of a Predator\u2013Prey Model with the Effect of Oscillation of Immigration of the Prey. Diversity, 13.","key":"ref_27","DOI":"10.3390\/d13010023"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1111\/1365-2656.12001","article-title":"Distinguishing between direct and indirect effects of predators in complex ecosystems","volume":"82","author":"Emmerson","year":"2013","journal-title":"J. Anim. Ecol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2450090","DOI":"10.1142\/S0218127424500901","article-title":"Hopf bifurcation and Turing instability of a delayed diffusive Zooplankton\u2013Phytoplankton model with hunting cooperation","volume":"34","author":"Meng","year":"2024","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1002\/mma.10325","article-title":"Impact of hunting cooperation in predator and anti-predator behaviors in prey in a predator\u2013prey model","volume":"48","author":"Li","year":"2024","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1121","DOI":"10.1017\/S0956792525000026","article-title":"Global well-posedness and Turing\u2013Hopf bifurcation of prey-taxis systems with hunting cooperation","volume":"36","author":"Tao","year":"2025","journal-title":"Eur. J. Appl. Math."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3275","DOI":"10.3934\/era.2024150","article-title":"The dynamics of a delayed predator-prey model with square root functional response and stage structure","volume":"32","author":"Peng","year":"2024","journal-title":"Electron. Res. Arch."},{"doi-asserted-by":"crossref","unstructured":"Naseer, A.H., and Bahlool, D.K. (2025). Dynamics of an Intraguild Predation Food Web Cooperation Model Under the Influence of Fear and Hunting. Computation, 13.","key":"ref_33","DOI":"10.3390\/computation13060128"},{"unstructured":"Waezizadeh, T., and Mehrpooya, A. (2016, January 28\u201331). A stochastic model for dynamics of two populations and its stability. Proceedings of the 47th Annual Iranian Mathematics Conference (AIMC47), Karaj, Iran.","key":"ref_34"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2559","DOI":"10.3934\/mbe.2025094","article-title":"Stability and bifurcation analysis in predator\u2013prey system involving Holling type-II functional response","volume":"22","author":"Ferreira","year":"2025","journal-title":"Math. Biosci. Eng."},{"key":"ref_36","first-page":"1546","article-title":"Impact of land use changes and habitat fragmentation on the eco-epidemiology of tick-borne diseases","volume":"58","author":"VanAcker","year":"2020","journal-title":"J. Med. 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