Spatiotemporal dynamics for impulsive eco-epidemiological model with Crowley-Martin type functional response

Haifeng Huo; Fanhong Zhang; Hong Xiang; Haifeng Huo; Fanhong Zhang; Hong Xiang

doi:10.3934/mbe.2022567

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 12180-12211. doi: 10.3934/mbe.2022567

Previous Article Next Article

Research article Special Issues

Spatiotemporal dynamics for impulsive eco-epidemiological model with Crowley-Martin type functional response

Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, China

Academic Editor: Xiang-Sheng Wang

Received: 13 July 2022 Revised: 02 August 2022 Accepted: 07 August 2022 Published: 19 August 2022

Spatiotemporal dynamics of an impulsive eco-epidemiological model with Crowley-Martin type functional responses in a heterogeneous space is studied. The ultimate boundedness of solutions is obtained. The conditions of persistence and extinction under impulsive controls are derived. Furthermore, the existence and globally asymptotic stability of a unique positive periodic solutions are proved. Numerical simulations are also shown to illustrate our theoretical results. Our results show that impulsive harvesting can accelerate the extinction of ecological epidemics.
- eco-epidemiological model,
- reaction-diffusion,
- Crowley-Martin type,
- impulsive effects,
- positive periodic solution
Citation: Haifeng Huo, Fanhong Zhang, Hong Xiang. Spatiotemporal dynamics for impulsive eco-epidemiological model with Crowley-Martin type functional response[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 12180-12211. doi: 10.3934/mbe.2022567

Related Papers:

Abstract

Spatiotemporal dynamics of an impulsive eco-epidemiological model with Crowley-Martin type functional responses in a heterogeneous space is studied. The ultimate boundedness of solutions is obtained. The conditions of persistence and extinction under impulsive controls are derived. Furthermore, the existence and globally asymptotic stability of a unique positive periodic solutions are proved. Numerical simulations are also shown to illustrate our theoretical results. Our results show that impulsive harvesting can accelerate the extinction of ecological epidemics.

References

[1]	A. M. Samoilenko, N. Perestyuk, Impulsive differential equations, World Scientific, 1995. https://doi.org/10.1142/2413
[2]	D. W. Rook, R. J. Fisher, Normative influences on impulsive buying behavior, J. Consum. Res., 22 (1995), 305–313. https://doi.org/10.1086/209452 doi: 10.1086/209452
[3]	X. Liu, L. Chen, Global dynamics of the periodic logistic system with periodic impulsive perturbations, J. Math. Anal. Appl., 289 (2004), 279–291. https://doi.org/10.1016/j.jmaa.2003.09.058 doi: 10.1016/j.jmaa.2003.09.058
[4]	J. J. Nieto, D. ORegan, Variational approach to impulsive differential equations, Nonlinear Anal.: Real World Appl., 10 (2009), 680–690. https://doi.org/10.1016/j.nonrwa.2007.10.022 doi: 10.1016/j.nonrwa.2007.10.022
[5]	S. Zavalishchin, A. N. Sesekin, Dynamic impulse systems: Theory and applications, Math. Appl., 394 (1997). https://doi.org/10.1007/978-94-015-8893-5 doi: 10.1007/978-94-015-8893-5
[6]	Y. Xie, Z. Wang, A ratio-dependent impulsive control of an SIQS epidemic model with non-linear incidence, Appl. Math. Comput., 423 (2022). https://doi.org/10.1016/j.amc.2022.127018 doi: 10.1016/j.amc.2022.127018
[7]	K. S. Jatav, J. Dhar, Hybrid approach for pest control with impulsive releasing of natural enemies and chemical pesticides: A plant-pest-natural enemy model, Nonlinear Anal.: Hybrid Syst., 12 (2014), 79–92. https://doi.org/10.1016/j.nahs.2013.11.011 doi: 10.1016/j.nahs.2013.11.011
[8]	K. Chakraborty, K. Das, H. Yu, Modeling and analysis of a modified leslie-gower type three species food chain model with an impulsive control strategy, Nonlinear Anal.: Hybrid Syst., 15 (2015), 171–184. https://doi.org/10.1016/j.nahs.2014.09.003 doi: 10.1016/j.nahs.2014.09.003
[9]	M. Zhao, X. Wang, H. Yu, J. Zhu, Dynamics of an ecological model with impulsive control strategy and distributed time delay, Math. Comput. Simul., 82 (2012), 1432–1444. https://doi.org/10.1016/j.matcom.2011.08.009 doi: 10.1016/j.matcom.2011.08.009
[10]	M. Fazly, M. Lewis, H. Wang, On impulsive reaction-diffusion models in higher dimensions, SIAM J. Appl. Math., 77 (2017). https://doi.org/10.1137/15M1046666 doi: 10.1137/15M1046666
[11]	J. Liang, Q. Yan, C. Xiang, S. Tang, A reaction-diffusion population growth equation with multiple pulse perturbations, Commun. Nonlinear Sci. Numer. Simul., 74 (2019), 122–137. https://doi.org/10.1016/j.cnsns.2019.02.015 doi: 10.1016/j.cnsns.2019.02.015
[12]	Y. Meng, Z. Lin, M. Pedersen, Effects of impulsive harvesting and an evolving domain in a diffusive logistic model, Nonlinearity, 34 (2021). https://doi.org/10.1088/1361-6544/ac1f78 doi: 10.1088/1361-6544/ac1f78
[13]	G. Liu, X. Meng, S. Liu, Dynamics for a tritrophic impulsive periodic plankton-fish system with diffusion in lakes, Math. Methods Appl. Sci., 44 (2021), 3260–3279. https://doi.org/10.1002/mma.6938 doi: 10.1002/mma.6938
[14]	Z. Liu, L. Zhang, P. Bi, J. Pang, B. Li, C. Fang, On the dynamics of one-prey-n-predator impulsive reaction-diffusion predator-prey system with ratio-dependent functional response, J. Biol. Dyn., 12 (2018), 551–576. https://doi.org/10.1080/17513758.2018.1485974 doi: 10.1080/17513758.2018.1485974
[15]	Z. Liu, S. Zhong, C. Yin, W. Chen, On the dynamics of an impulsive reaction-diffusion predator-prey system with ratio-dependent functional response, Acta Appl. Math., 115 (2011), 329–349. https://doi.org/10.1007/s10440-011-9624-8 doi: 10.1007/s10440-011-9624-8
[16]	C. Dai, H. Liu, Z. Jin, Q. Guo, Y. Wang, H. Yu, et al., Dynamic analysis of a heterogeneous diffusive prey-predator system in time-periodic environment, Complexity, 2020 (2020). https://doi.org/10.1155/2020/7134869 doi: 10.1155/2020/7134869
[17]	H. Liu, H. Yu, C. Dai, Q. Wang, J. Li, R. P. Agarwal, et al., Dynamic analysis of a reaction-diffusion impulsive hybrid system, Nonlinear Anal.: Hybrid Syst., 33 (2019), 353–370. https://doi.org/10.1016/j.nahs.2019.03.001 doi: 10.1016/j.nahs.2019.03.001
[18]	X. Li, Q. Wang, R. Han, An impulsive predator-prey system with modified leslie-gower functional response and diffusion, Qual. Theory Dyn. Syst., 20 (2021). https://doi.org/10.1007/s12346-021-00517-2 doi: 10.1007/s12346-021-00517-2
[19]	Z. Liu, S. Zhong, X. Liu, Permanence and periodic solutions for an impulsive reaction-diffusion food-chain system with ratio-dependent functional response, Commun. Nonlinear Sci. Numer. Simul., 19 (2014), 173–188. https://doi.org/10.1016/j.cnsns.2013.05.030 doi: 10.1016/j.cnsns.2013.05.030
[20]	P. H. Crowley, E. K. Martin, Functional responses and interference within and between year classes of a dragonfly population, J. North Am. Benthol. Soc., 8 (1989). https://doi.org/10.2307/1467324 doi: 10.2307/1467324
[21]	Q. Dong, W. Ma, M. Sun, The asymptotic behavior of a chemostat model with crowley-Martin type functional response and time delays, J. Math. Chem., 51 (2013), 1231–1248. https://doi.org/10.1007/s10910-012-0138-z doi: 10.1007/s10910-012-0138-z
[22]	X. Liu, S. Zhong, B. Tian, F. Zheng, Asymptotic properties of a stochastic predator-prey model with Crowley-Martin functional response, J. Appl. Math. Comput., 43 (2013), 479–490. https://doi.org/10.1007/s12190-013-0674-0 doi: 10.1007/s12190-013-0674-0
[23]	X. Li, X. Lin, J. Liu, Existence and global attractivity of positive periodic solutions for a predator-prey model with Crowley-Martin functional response, Electron. J. Differ. Equations, 2018 (2018), 1–17. Available from: https://ejde.math.txstate.edu/Volumes/2018/191/li.pdf.
[24]	R. K. Upadhyay, R. K. Naji, Dynamics of a three species food chain model with Crowley-Martin type functional response, Chaos, Solitons Fractals, 42 (2009), 1337–1346. https://doi.org/10.1016/j.chaos.2009.03.020 doi: 10.1016/j.chaos.2009.03.020
[25]	X. Shi, X. Zhou, X. Song, Analysis of a stage-structured predator-prey model with Crowley-Martin function, J. Appl. Math. Comput., 36 (2011), 459–472. https://doi.org/10.1007/s12190-010-0413-8 doi: 10.1007/s12190-010-0413-8
[26]	Y. Xie, Z. Wang, Transmission dynamics, global stability and control strategies of a modified SIS epidemic model on complex networks with an infective medium, Math. Comput. Simul., 188 (2021), 23–34. https://doi.org/10.1016/j.matcom.2021.03.029 doi: 10.1016/j.matcom.2021.03.029
[27]	M. Cai, S. Yan, Z. Du, Positive periodic solutions of an eco-epidemic model with Crowley-Martin type functional response and disease in the prey, Qual. Theory Dyn. Syst., 19 (2020). https://doi.org/10.1007/s12346-020-00392-3 doi: 10.1007/s12346-020-00392-3
[28]	Z. Chang, X. Xing, S. Liu, X. Meng, Spatiotemporal dynamics for an impulsive eco-epidemiological system driven by canine distemper virus, Appl. Math. Comput., 402 (2021). https://doi.org/10.1016/j.amc.2021.126135 doi: 10.1016/j.amc.2021.126135
[29]	H. Smith, Dynamics of competition, Math. Inspired Biol., 1714 (1999), 191–240. https://doi.org/10.1007/BFb0092378 doi: 10.1007/BFb0092378
[30]	W. Walter, Differential inequalities and maximum principles: Theory, new methods and applications, Nonlinear Anal.: Theory Methods Appl., 30 (1997), 4695–4711. https://doi.org/10.1016/S0362-546X(96)00259-3 doi: 10.1016/S0362-546X(96)00259-3
[31]	M. Akhmet, M. Beklioglu, T. Ergenc, V. Tkachenko, An impulsive ratio-dependent predator-prey system with diffusion, Nonlinear Anal.: Real World Appl., 7 (2006), 1255–1267. https://doi.org/10.1016/j.nonrwa.2005.11.007 doi: 10.1016/j.nonrwa.2005.11.007
[32]	D. Henry, Geometric theory of semilinear parabolic equations, Springer, 840 (2006). https://doi.org/10.1007/bfb0089647 doi: 10.1007/bfb0089647
[33]	O. Struk, V. Tkachenko, On impulsive lotka-volterra systems with diffusion, Ukr. Math. J., 54 (2002), 629–646. https://doi.org/10.1023/A:1021039528818 doi: 10.1023/A:1021039528818
[34]	M. A. Krasnoselskij, P. P. Zabrejko, Geometrical methods of nonlinear analysis, Springer, 263 (1984).

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)