Research article Special Issues

Dynamics and optimal control of a stochastic Zika virus model with spatial diffusion


  • Received: 14 July 2023 Revised: 15 August 2023 Accepted: 29 August 2023 Published: 13 September 2023
  • Zika is an infectious disease with multiple transmission routes, which is related to severe congenital disabilities, especially microcephaly, and has attracted worldwide concern. This paper aims to study the dynamic behavior and optimal control of the disease. First, we establish a stochastic reaction-diffusion model (SRDM) for Zika virus, including human-mosquito transmission, human-human sexual transmission, and vertical transmission of mosquitoes, and prove the existence, uniqueness, and boundedness of the global positive solution of the model. Then, we discuss the sufficient conditions for disease extinction and the existence of a stationary distribution of positive solutions. After that, three controls, i.e. personal protection, treatment of infected persons, and insecticides for spraying mosquitoes, are incorporated into the model and an optimal control problem of Zika is formulated to minimize the number of infected people, mosquitoes, and control cost. Finally, some numerical simulations are provided to explain and supplement the theoretical results obtained.

    Citation: Minna Shao, Hongyong Zhao. Dynamics and optimal control of a stochastic Zika virus model with spatial diffusion[J]. Mathematical Biosciences and Engineering, 2023, 20(9): 17520-17553. doi: 10.3934/mbe.2023778

    Related Papers:

    [1] Baoye Song, Shumin Tang, Yao Li . A new path planning strategy integrating improved ACO and DWA algorithms for mobile robots in dynamic environments. Mathematical Biosciences and Engineering, 2024, 21(2): 2189-2211. doi: 10.3934/mbe.2024096
    [2] Jian Si, Xiaoguang Bao . A novel parallel ant colony optimization algorithm for mobile robot path planning. Mathematical Biosciences and Engineering, 2024, 21(2): 2568-2586. doi: 10.3934/mbe.2024113
    [3] Yuzhuo Shi, Huijie Zhang, Zhisheng Li, Kun Hao, Yonglei Liu, Lu Zhao . Path planning for mobile robots in complex environments based on improved ant colony algorithm. Mathematical Biosciences and Engineering, 2023, 20(9): 15568-15602. doi: 10.3934/mbe.2023695
    [4] Zhen Yang, Junli Li, Liwei Yang, Qian Wang, Ping Li, Guofeng Xia . Path planning and collision avoidance methods for distributed multi-robot systems in complex dynamic environments. Mathematical Biosciences and Engineering, 2023, 20(1): 145-178. doi: 10.3934/mbe.2023008
    [5] Tian Xue, Liu Li, Liu Shuang, Du Zhiping, Pang Ming . Path planning of mobile robot based on improved ant colony algorithm for logistics. Mathematical Biosciences and Engineering, 2021, 18(4): 3034-3045. doi: 10.3934/mbe.2021152
    [6] Xuewu Wang, Bin Tang, Xin Zhou, Xingsheng Gu . Double-robot obstacle avoidance path optimization for welding process. Mathematical Biosciences and Engineering, 2019, 16(5): 5697-5708. doi: 10.3934/mbe.2019284
    [7] Zhenao Yu, Peng Duan, Leilei Meng, Yuyan Han, Fan Ye . Multi-objective path planning for mobile robot with an improved artificial bee colony algorithm. Mathematical Biosciences and Engineering, 2023, 20(2): 2501-2529. doi: 10.3934/mbe.2023117
    [8] Ping Li, Liwei Yang . Conflict-free and energy-efficient path planning for multi-robots based on priority free ant colony optimization. Mathematical Biosciences and Engineering, 2023, 20(2): 3528-3565. doi: 10.3934/mbe.2023165
    [9] Jinzhuang Xiao, Xuele Yu, Keke Sun, Zhen Zhou, Gang Zhou . Multiobjective path optimization of an indoor AGV based on an improved ACO-DWA. Mathematical Biosciences and Engineering, 2022, 19(12): 12532-12557. doi: 10.3934/mbe.2022585
    [10] Chikun Gong, Yuhang Yang, Lipeng Yuan, Jiaxin Wang . An improved ant colony algorithm for integrating global path planning and local obstacle avoidance for mobile robot in dynamic environment. Mathematical Biosciences and Engineering, 2022, 19(12): 12405-12426. doi: 10.3934/mbe.2022579
  • Zika is an infectious disease with multiple transmission routes, which is related to severe congenital disabilities, especially microcephaly, and has attracted worldwide concern. This paper aims to study the dynamic behavior and optimal control of the disease. First, we establish a stochastic reaction-diffusion model (SRDM) for Zika virus, including human-mosquito transmission, human-human sexual transmission, and vertical transmission of mosquitoes, and prove the existence, uniqueness, and boundedness of the global positive solution of the model. Then, we discuss the sufficient conditions for disease extinction and the existence of a stationary distribution of positive solutions. After that, three controls, i.e. personal protection, treatment of infected persons, and insecticides for spraying mosquitoes, are incorporated into the model and an optimal control problem of Zika is formulated to minimize the number of infected people, mosquitoes, and control cost. Finally, some numerical simulations are provided to explain and supplement the theoretical results obtained.





    [1] G. W. A. Dick, S. F. Kitchen, A. J. Haddow, Zika virus (Ⅰ). Isolations and serological specificity, Trans. R. Soc. Trop. Med. Hyg., 46 (1952), 509–-520. https://doi.org/10.1016/0035-9203(52)90042-4 doi: 10.1016/0035-9203(52)90042-4
    [2] F. N. Macnamara, Zika virus: a report on three cases of human infection during an epidemic of jaundice in Nigeria, Trans. R. Soc. Trop. Med. Hyg., 48 (1954), 139–145. https://doi.org/10.1016/0035-9203(54)90006-1 doi: 10.1016/0035-9203(54)90006-1
    [3] J. G. Olson, T. G. Ksiazek, Suhandiman, Triwibowo, Zika virus, a cause of fever in Central Java, Indonesia, Trans. R. Soc. Trop. Med. Hyg., 75 (1981), 389–393. https://doi.org/10.1016/0035-9203(81)90100-0 doi: 10.1016/0035-9203(81)90100-0
    [4] M. R. Duffy, T. H. Chen, W. T. Hancock, A. M. Powers, J. L. Kool, R. S. Lanciotti, et al., Zika virus outbreak on Yap Island, federated states of Micronesia, New. Eng. J. Med., 360 (2009), 2536–2543. https://doi.org/10.1056/NEJMoa0805715 doi: 10.1056/NEJMoa0805715
    [5] C. Zanluca, V. C. A. d. Melo, A. L. P. Mosimann, G. I. V. d. Santos, C. N. D. d. Santos, K. Luz, First report of autochthonous transmission of Zika virus in Brazil, Mem. I. Oswaldo. Cruz., 110 (2015), 569–572. https://doi.org/10.1590/0074-02760150192 doi: 10.1590/0074-02760150192
    [6] J. Rocklöv, M. B. Quam, B. Sudre, M. German, M. U. G. Kraemer, O. Brady, et al., Assessing seasonal risks for the introduction and mosquito-borne spread of Zika virus in Europe, EBioMedicine, 9 (2016), 250–256. https://doi.org/10.1016/j.ebiom.2016.06.009 doi: 10.1016/j.ebiom.2016.06.009
    [7] P. Watson-Brown, E. Viennet, G. Mincham, C. R. Williams, C. C. Jansen, B. L. Montgomery, et al., Epidemic potential of Zika virus in Australia: implications for blood transfusion safety, Transfusion, 59 (2019), 648–658. https://doi.org/10.1111/trf.15095 doi: 10.1111/trf.15095
    [8] Centers for Diease Control and Prevention, Zika virus, 2018. Available from: https://www.cdc.gov/zika/.
    [9] J. Tataryn, L. Vrbova, M. Drebot, H. Wood, E. Payne, S. Connors, et al., Travel-related Zika virus cases in Canada: October 2015-June 2017, Can. Commun. Dis. Rep., 44 (2018), 18–26. https://doi.org/10.14745/ccdr.v44i01a05 doi: 10.14745/ccdr.v44i01a05
    [10] T. Hashimoto, S. Kutsuna, S. Tajima, E. Nakayama, T. Maeki, S. Taniguchi, et al., Importation of Zika Virus from Vietnam to Japan, November 2016, emphEmerg. Infect. Dis., 23 (2017), 1223–1225. https://doi.org/10.3201/eid2307.170519 doi: 10.3201/eid2307.170519
    [11] H. Jia, M. Zhang, M. Chen, Z. Yang, J. Li, G. Huang, et al., Zika virus infection in travelers returning from coutries with local transmission, Guangdong, China, 2016, Travel Med. Infect. Dis., 21 (2018), 56–61. https://doi.org/10.1016/j.tmaid.2017.11.012 doi: 10.1016/j.tmaid.2017.11.012
    [12] H. Singh, O. P. Singh, N. Akhtar, G. Sharma, A. Sindhania, N. Gupta, et al., First report on the transmission of Zika virus by Aedes (Stegomyia) aegypti (L.) (Diptera: Culicidae) during the 2018 Zika outbreak in India, Acta Trop., 199 (2019), 1–6. https://doi.org/10.1016/j.actatropica.2019.105114 doi: 10.1016/j.actatropica.2019.105114
    [13] International Travel Health Advisory Network, 2022. Available from: https://www.ithc.cn/article/460057.html.
    [14] World Health Organization, Zika virus, 2018. Available from: https://www.who.int/mediacentre/factsheets/zika/en/.
    [15] K. Russell, S. L. Hills, A. M. Oster, C. C. Porse, G. Danyluk, M. Cone, et al., Male-to-female sexual transmission of Zika virus-United States, January-April 2016, Clin. Infect. Dis., 64 (2017), 211–213. https://doi.org/10.1093/cid/ciw692 doi: 10.1093/cid/ciw692
    [16] D. T. Deckard, W. M. Chung, J. T. Brooks, J. C. Smith, S. Woldai, M. Hennessey, et al., Male-to-male sexual transmission of Zika virus-Texas, January 2016, MMWR-Morbid. Mortal. W., 65 (2016), 371–374. http://dx.doi.org/10.15585/mmwr.mm6514a3 doi: 10.15585/mmwr.mm6514a3
    [17] S. Thangamani, J. Huang, C. E. Hart, H. Guzman, R. B. Tesh, Vertical transmission of Zika virus in Aedes aegypti mosquitoes, Am. J. Trop. Med. Hyg., 95 (2016), 1169–1173. https://doi.org/10.4269/ajtmh.16-0448 doi: 10.4269/ajtmh.16-0448
    [18] S. Du, Y. Liu, J. Liu, J. Zhao, C. Champagne, L. Tong, et al., Aedes mosquitoes acquire and transmit Zika virus by breeding in contaminated aquatic environments, Nat. Commun., 10 (2019), 1–11. https://doi.org/10.1038/s41467-019-09256-0 doi: 10.1038/s41467-019-09256-0
    [19] Microcephaly Epidemic Research Group, Microcephaly in infants, Pernambuco state, Brazil, 2015, Emerg. Infect. Dis., 22 (2016), 1090–1093. https://doi.org/10.3201/eid2206.160062
    [20] L. S. Munoz, P. Barreras, C. A. Pardo, Zika virus-associated neurological disease in the adult: Guillain-Barré syndrome, encephalitis, and myelitis, Semin. Reprod. Med., 34 (2016), 273–279. https://dx.doi.org/10.1055/s-0036-1592066 doi: 10.1055/s-0036-1592066
    [21] F. Brauer, C. Castillo-Chavez, Mathematical models in population biology and epidemiology, Springer Press, 2001.
    [22] D. Gao, Y. Lou, D. He, T. C. Porco, Y. Kuang, G. Chowell, et al., Prevention and control of Zika as a mosquito-borne and sexually transmitted disease: A mathematical modeling analysis, Sci. Rep., 6 (2016), 1–6. https://doi.org/10.1038/srep28070 doi: 10.1038/srep28070
    [23] F. B. Agusto, S. Bewick, W. F. Fagan, Mathematical model of zika virus with vertical transmission, Infec. Dis. Model, 2 (2017), 244–267. https://doi.org/10.1016/j.idm.2017.05.003 doi: 10.1016/j.idm.2017.05.003
    [24] H. Zhao, L. Wang, S. M. Oliva, H. Zhu, Modeling and dynamics analysis of Zika transmission with limited medical resources, B. Math. Biol., 82 (2020), 99. https://doi.org/10.1007/s11538-020-00776-1 doi: 10.1007/s11538-020-00776-1
    [25] L. Wang, H. Zhao, S. M. Oliva, H. Zhu, Modeling the transmission and control of Zika in Brazil, Sci. Rep-UK, 7 (2017), 7721. https://doi.org/10.1038/s41598-017-07264-y doi: 10.1038/s41598-017-07264-y
    [26] X. Yuan, Y. Lou, D. He, J. Wang, D. Gao, A Zika Endemic Model for the Contribution of Multiple Transmission Routes, B. Math. Biol., 83 (2021), 111. https://doi.org/10.1007/s11538-021-00945-w doi: 10.1007/s11538-021-00945-w
    [27] L. Wang, H. Zhao, Modeling and dynamics analysis of Zika transmission with contaminated aquatic environments, Nonlinear Dynam., 104 (2021), 845–862. https://doi.org/10.1007/s11071-021-06289-3 doi: 10.1007/s11071-021-06289-3
    [28] W. Fitzgibbon, J. Morgan, G. Webb, An outbreak vector-host epidemic model with spatial structure: the 2015–2016 Zika outbreak in Rio De Janeiro, Theor. Biol. Med. Model, 14 (2017), 7. https://doi.org/10.1186/s12976-017-0051-z doi: 10.1186/s12976-017-0051-z
    [29] Y. Cai, K. Wang, W. Wang, Global transmission dynamics of a Zika virus model, Appl. Math. Lett., 92 (2019), 190–195. https://doi.org/10.1016/j.aml.2019.01.015 doi: 10.1016/j.aml.2019.01.015
    [30] F. Li, X. Zhao, Global dynamics of a reaction–diffusion model of Zika virus transmission with seasonality, B. Math. Biol., 83 (2021), 43. https://doi.org/10.1007/s11538-021-00879-3 doi: 10.1007/s11538-021-00879-3
    [31] Y. Zhao, D. Jiang, The threshold of a stochastic SIS epidemic model with vaccination, Appl. Math. Comput., 243 (2014), 718–727. https://doi.org/10.1016/j.amc.2014.05.124 doi: 10.1016/j.amc.2014.05.124
    [32] Z. Shi, X. Zhang, D. Jiang, Dynamics of an avian influenza model with half-saturated incidence, Appl. Math. Comput., 355 (2019), 399–416. https://doi.org/10.1016/j.amc.2019.02.070 doi: 10.1016/j.amc.2019.02.070
    [33] L. Xue, X. Cao, H. Wan, Releasing Wolbachia-infected mosquitos to mitigate the transmission of Zika virus, J. Math. Anal. Appl., 496 (2021), 124804 https://doi.org/10.1016/j.jmaa.2020.124804 doi: 10.1016/j.jmaa.2020.124804
    [34] X. Ran, L. Hu, L. Nie, Z. Teng, Effects of stochastic perturbation and vaccinated age on a vector-borne epidemic model with saturation incidence rate, Appl. Math. Comput., 394 (2021), 125798. https://doi.org/10.1016/j.amc.2020.125798 doi: 10.1016/j.amc.2020.125798
    [35] T. Y. Miyaoka, S. Lenhart, J. F. C. A. Meyer, Optimal control of vaccination in a vector-borne reaction–diffusion model applied to Zika virus, J. Math. Biol., 79 (2019), 1077–1104. https://doi.org/10.1007/s00285-019-01390-z doi: 10.1007/s00285-019-01390-z
    [36] E. Bonyah, M. A. Khan, K. O. Okosun, S. Islam, A theoretical model for Zika virus transmission, Plos One, 12 (2017), e0185540. https://doi.org/10.1371/journal.pone.0185540 doi: 10.1371/journal.pone.0185540
    [37] M. A. Khan, S. W. Shah, S. Ullah, J. F. Gómez-Aguilar, A dynamical model of asymptomatic carrier zika virus with optimal control strategies, Nonlinear Anal-Real., 50 (2019), 144–170. https://doi.org/10.1016/j.nonrwa.2019.04.006 doi: 10.1016/j.nonrwa.2019.04.006
    [38] C. A. Manore, K. S. Hickmann, S. Xu, H. J. Wearing, J. M. Hyman, Comparing dengue and chikungunya emergence and endemic transmission in A. aegypti and A. albopictus, J. Theor. Biol., 356 (2014), 174–191. https://doi.org/10.1016/j.jtbi.2014.04.033 doi: 10.1016/j.jtbi.2014.04.033
    [39] L. Xue, X. Fang, J. M. Hyman, Comparing the effectiveness of different strains of Wolbachia for controlling chikungunya, dengue fever, and zika, PLos. Negl. Trop. Dis., 12 (2018), e0006666. https://doi.org/10.1371/journal.pntd.0006666 doi: 10.1371/journal.pntd.0006666
    [40] M. Besnard, S. Lastere, A. Teissier, V. Cao-Lormeau, D. Musso, Evidence of perinatal transmission of Zika virus, French Polynesia, December 2013 and February 2014, Eurosurveillance, 19 (2014), 20751. https://doi.org/10.2807/1560-7917.ES2014.19.13.20751 doi: 10.2807/1560-7917.ES2014.19.13.20751
    [41] C. Bowman, A. B. Gumel, P. van den Driessche, J. Wu, H. Zhu, A mathematical model for assessing control strategies against West Nile virus, B. Math. Biol., 67 (2005), 1107–1133. https://doi.org/10.1016/j.bulm.2005.01.002 doi: 10.1016/j.bulm.2005.01.002
    [42] M. Andraud, N. Hens, C. Marais, P. Beutels, Dynamic epidemiological models for dengue transmission: a systematic review of structural approaches, Plos One, 7 (2012), e49085. https://doi.org/10.1371/journal.pone.0049085 doi: 10.1371/journal.pone.0049085
    [43] E. Chikaki, H. Ishikawa, A dengue transmission model in Tailand considering sequential infections with all four serotypes, J. Infect. Dev. Countr., 3 (2009), 711–722. https://doi.org/10.3855/jidc.616 doi: 10.3855/jidc.616
    [44] X. Mao, Stochastic differential equations and applications, second edition, Horwood Press, Chichester, 2007.
    [45] K. Liu, Stationary distributions of second order stochastic evolution equations with memory in Hilbert spaces, Stoch. Proc. Appl., 130 (2020), 366–393. https://doi.org/10.1016/j.spa.2019.03.015 doi: 10.1016/j.spa.2019.03.015
    [46] R. M. Dudley, Real Analysis and Probability, second edition, Cambridge University Press, 2003.
    [47] H. J. Kushner, Existence results for optimal stochastic controls, J. Optim. Theory. Appl., 15 (1975), 347–359. https://doi.org/10.1007/BF00933203 doi: 10.1007/BF00933203
    [48] J. Yong, X. Zhou, Stochastic Control: Hamiltonian Systems and HJB Equations, Springer Press, 1999.
    [49] D. J. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Rev., 43 (2001), 525–546. https://doi.org/10.1137/s0036144500378302 doi: 10.1137/s0036144500378302
    [50] O. J. Brady, M. A. Johansson, C. A. Guerra, S. Bhatt, N. Golding, D. M. Pigott, et al., Modelling adult Aedes aegypti and Aedes albopictus survival at different temperatures in laboratory and field settings, Parasite. Vector., 6 (2013), 351. https://doi.org/10.1186/1756-3305-6-351 doi: 10.1186/1756-3305-6-351
  • This article has been cited by:

    1. Liwei Yang, Lixia Fu, Ping Li, Jianlin Mao, Ning Guo, An Effective Dynamic Path Planning Approach for Mobile Robots Based on Ant Colony Fusion Dynamic Windows, 2022, 10, 2075-1702, 50, 10.3390/machines10010050
    2. Qian Wang, Junli Li, Liwei Yang, Zhen Yang, Ping Li, Guofeng Xia, Distributed Multi-Mobile Robot Path Planning and Obstacle Avoidance Based on ACO–DWA in Unknown Complex Terrain, 2022, 11, 2079-9292, 2144, 10.3390/electronics11142144
    3. Pranshav Gajjar, Virensinh Dodia, Siddharth Mandaliya, Pooja Shah, Vijay Ukani, Madhu Shukla, 2022, Chapter 19, 978-3-031-23094-3, 262, 10.1007/978-3-031-23095-0_19
    4. Xingcheng Pu, Xinlin Song, Ling Tan, Yi Zhang, Improved ant colony algorithm in path planning of a single robot and multi-robots with multi-objective, 2023, 1864-5909, 10.1007/s12065-023-00821-7
    5. Xiaoling Meng, Xijing Zhu, Autonomous Obstacle Avoidance Path Planning for Grasping Manipulator Based on Elite Smoothing Ant Colony Algorithm, 2022, 14, 2073-8994, 1843, 10.3390/sym14091843
    6. Sai Zhang, Li Tang, Yan-Jun Liu, Formation deployment control of multi-agent systems modeled with PDE, 2022, 19, 1551-0018, 13541, 10.3934/mbe.2022632
    7. Jie Zhang, Xiuqin Pan, 2022, Chapter 1, 978-3-031-23584-9, 3, 10.1007/978-3-031-23585-6_1
    8. Zhen Yang, Junli Li, Liwei Yang, Qian Wang, Ping Li, Guofeng Xia, Path planning and collision avoidance methods for distributed multi-robot systems in complex dynamic environments, 2022, 20, 1551-0018, 145, 10.3934/mbe.2023008
    9. Nour Abujabal, Raouf Fareh, Saif Sinan, Mohammed Baziyad, Maamar Bettayeb, A comprehensive review of the latest path planning developments for multi-robot formation systems, 2023, 0263-5747, 1, 10.1017/S0263574723000322
    10. Yiqi Xu, Qiongqiong Li, Xuan Xu, Jiafu Yang, Yong Chen, Research Progress of Nature-Inspired Metaheuristic Algorithms in Mobile Robot Path Planning, 2023, 12, 2079-9292, 3263, 10.3390/electronics12153263
    11. Wenjie Ning, Li Ma, Zhichuang Wang, Fangyuan Hou, 2024, Chapter 33, 978-981-97-3327-9, 393, 10.1007/978-981-97-3328-6_33
    12. Semonti Banik, Sajal Chandra Banik, Sarker Safat Mahmud, Path Planning Approaches in Multi‐robot System: A Review, 2024, 2577-8196, 10.1002/eng2.13035
    13. Georgios Karamitsos, Dimitrios Bechtsis, Naoum Tsolakis, Dimitrios Vlachos, 2024, Chapter 5, 978-3-031-58918-8, 139, 10.1007/978-3-031-58919-5_5
    14. Liwei Yang, Ping Li, Song Qian, He Quan, Jinchao Miao, Mengqi Liu, Yanpei Hu, Erexidin Memetimin, Path Planning Technique for Mobile Robots: A Review, 2023, 11, 2075-1702, 980, 10.3390/machines11100980
    15. Bilal Gurevin, Furkan Gulturk, Muhammed Yildiz, Ihsan Pehlivan, Trung Thanh Nguyen, Fatih Caliskan, Baris Boru, Mustafa Zahid Yildiz, A Novel GUI Design for Comparison of ROS-Based Mobile Robot Local Planners, 2023, 11, 2169-3536, 125738, 10.1109/ACCESS.2023.3327705
    16. Zhen Zhou, Chenchen Geng, Buhu Qi, Aiwen Meng, Jinzhuang Xiao, Research and experiment on global path planning for indoor AGV via improved ACO and fuzzy DWA, 2023, 20, 1551-0018, 19152, 10.3934/mbe.2023846
    17. Mohammed Baziyad, Nour AbuJabal, Raouf Fareh, Tamer Rabie, Ibrahim Kamel, Maamar Bettayeb, 2023, A Direction for Swarm Robotic Path Planning Technique Using Potential Field Concepts and Particle Swarm Optimization, 979-8-3503-8239-6, 7, 10.1109/IIT59782.2023.10366467
    18. Shuai Wu, Ani Dong, Qingxia Li, Wenhong Wei, Yuhui Zhang, Zijing Ye, Application of ant colony optimization algorithm based on farthest point optimization and multi-objective strategy in robot path planning, 2024, 167, 15684946, 112433, 10.1016/j.asoc.2024.112433
    19. Yongrong Cai, Haibin Liu, Mingfei Li, Fujie Ren, A Method of Dual-AGV-Ganged Path Planning Based on the Genetic Algorithm, 2024, 14, 2076-3417, 7482, 10.3390/app14177482
    20. Shuai Wu, Qingxia Li, Wenhong Wei, Zijing Ye, 2023, Research on Mobile Robot Path Planning in Angle-Guided Ant Colony Optimization Algorithm, 979-8-3503-0375-9, 7070, 10.1109/CAC59555.2023.10450803
    21. Nour AbuJabal, Tamer Rabie, Mohammed Baziyad, Ibrahim Kamel, Khawla Almazrouei, Path Planning Techniques for Real-Time Multi-Robot Systems: A Systematic Review, 2024, 13, 2079-9292, 2239, 10.3390/electronics13122239
    22. Nour Ayman Abujabal, Tamer Rabie, Ibrahim Kamel, 2023, Path Planning Techniques for Multi-robot Systems: A Systematic Review, 979-8-3503-8239-6, 1, 10.1109/IIT59782.2023.10366472
    23. Cuicui Cai, Chaochuan Jia, Yao Nie, Jinhong Zhang, Ling Li, A path planning method using modified harris hawks optimization algorithm for mobile robots, 2023, 9, 2376-5992, e1473, 10.7717/peerj-cs.1473
    24. Shuai Wu, Qingxia Li, Wenhong Wei, Application of Ant Colony Optimization Algorithm Based on Triangle Inequality Principle and Partition Method Strategy in Robot Path Planning, 2023, 12, 2075-1680, 525, 10.3390/axioms12060525
    25. Meltem Eyuboglu, Gokhan Atali, A novel collaborative path planning algorithm for 3-wheel omnidirectional Autonomous Mobile Robot, 2023, 169, 09218890, 104527, 10.1016/j.robot.2023.104527
    26. Wenteng Wang, 2024, Chapter 4, 978-981-97-3209-8, 39, 10.1007/978-981-97-3210-4_4
    27. Haobo Feng, Qiao Hu, Zhenyi Zhao, Xinglong Feng, Chuan Jiang, A varied-width path planning method for multiple AUV formation, 2025, 199, 03608352, 110746, 10.1016/j.cie.2024.110746
    28. Luis E. Ruiz-Fernandez, Javier Ruiz-Leon, David Gomez-Gutierrez, Rafael Murrieta-Cid, Decentralized multi-robot formation control in environments with non-convex and dynamic obstacles based on path planning algorithms, 2025, 1861-2776, 10.1007/s11370-024-00582-x
    29. Yong Li, Neng Long, 2024, Path Planning for Mobile Robots Based on the Improved Adaptive Ant Colony Algorithm, 979-8-3503-6860-4, 1761, 10.1109/CAC63892.2024.10865367
    30. Wenyan Zhu, Wenzheng Cai, Hoiio Kong, Optimal Path Planning Based on ACO in Intelligent Transportation, 2025, 26663074, 10.1016/j.ijcce.2025.02.006
    31. Huiliao Yang, Bo Zhang, Chang Xiao, 2025, Chapter 44, 978-981-96-2227-6, 470, 10.1007/978-981-96-2228-3_44
    32. Guangping Qiu, Jizhong Deng, Jincan Li, Weixing Wang, Hybrid Clustering-Enhanced Brain Storm Optimization Algorithm for Efficient Multi-Robot Path Planning, 2025, 10, 2313-7673, 347, 10.3390/biomimetics10060347
  • Reader Comments
  • © 2023 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)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(1682) PDF downloads(166) Cited by(1)

Article outline

Figures and Tables

Figures(11)  /  Tables(1)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog