{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T01:30:05Z","timestamp":1789522205364,"version":"build-2803163510"},"reference-count":50,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"9","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MBE"],"published-print":{"date-parts":[[2023]]},"abstract":"<jats:p xml:lang=\"fr\">&lt;abstract&gt;&lt;p&gt;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.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/mbe.2023778","type":"journal-article","created":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T10:41:54Z","timestamp":1694601714000},"page":"17520-17553","source":"Crossref","is-referenced-by-count":2,"title":["Dynamics and optimal control of a stochastic Zika virus model with spatial diffusion"],"prefix":"10.3934","volume":"20","author":[{"given":"Minna","family":"Shao","sequence":"first","affiliation":[{"name":"College of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"},{"name":"College of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongyong","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"},{"name":"Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing 211106, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2321","reference":[{"key":"key-10.3934\/mbe.2023778-1","doi-asserted-by":"publisher","unstructured":"G. W. A. Dick, S. F. Kitchen, A. J. Haddow, Zika virus (\u2160). Isolations and serological specificity, <i>Trans. R. Soc. Trop. Med. Hyg.<\/i>, <b>46<\/b> (1952), 509\u2013-520. https:\/\/doi.org\/10.1016\/0035-9203(52)90042-4","DOI":"10.1016\/0035-9203(52)90042-4"},{"key":"key-10.3934\/mbe.2023778-2","doi-asserted-by":"publisher","unstructured":"F. N. Macnamara, Zika virus: a report on three cases of human infection during an epidemic of jaundice in Nigeria, <i>Trans. R. Soc. Trop. Med. Hyg.<\/i>, <b>48<\/b> (1954), 139\u2013145. https:\/\/doi.org\/10.1016\/0035-9203(54)90006-1","DOI":"10.1016\/0035-9203(54)90006-1"},{"key":"key-10.3934\/mbe.2023778-3","doi-asserted-by":"publisher","unstructured":"J. G. Olson, T. G. Ksiazek, Suhandiman, Triwibowo, Zika virus, a cause of fever in Central Java, Indonesia, <i>Trans. R. Soc. Trop. Med. Hyg.<\/i>, <b>75<\/b> (1981), 389\u2013393. https:\/\/doi.org\/10.1016\/0035-9203(81)90100-0","DOI":"10.1016\/0035-9203(81)90100-0"},{"key":"key-10.3934\/mbe.2023778-4","doi-asserted-by":"publisher","unstructured":"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, <i>New. Eng. J. Med<\/i>., <b>360<\/b> (2009), 2536\u20132543. https:\/\/doi.org\/10.1056\/NEJMoa0805715","DOI":"10.1056\/NEJMoa0805715"},{"key":"key-10.3934\/mbe.2023778-5","doi-asserted-by":"publisher","unstructured":"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, <i>Mem. I. Oswaldo. Cruz.<\/i>, <b>110<\/b> (2015), 569\u2013572. https:\/\/doi.org\/10.1590\/0074-02760150192","DOI":"10.1590\/0074-02760150192"},{"key":"key-10.3934\/mbe.2023778-6","doi-asserted-by":"publisher","unstructured":"J. Rockl\u00f6v, 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, <i>EBioMedicine<\/i>, <b>9<\/b> (2016), 250\u2013256. https:\/\/doi.org\/10.1016\/j.ebiom.2016.06.009","DOI":"10.1016\/j.ebiom.2016.06.009"},{"key":"key-10.3934\/mbe.2023778-7","doi-asserted-by":"publisher","unstructured":"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, <i>Transfusion<\/i>, <b>59<\/b> (2019), 648\u2013658. https:\/\/doi.org\/10.1111\/trf.15095","DOI":"10.1111\/trf.15095"},{"key":"key-10.3934\/mbe.2023778-8","unstructured":"<i>Centers for Diease Control and Prevention<\/i>, Zika virus, 2018. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.cdc.gov\/zika\/\">https:\/\/www.cdc.gov\/zika\/<\/ext-link>."},{"key":"key-10.3934\/mbe.2023778-9","doi-asserted-by":"publisher","unstructured":"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, <i>Can. Commun. Dis. Rep<\/i>., <b>44<\/b> (2018), 18\u201326. https:\/\/doi.org\/10.14745\/ccdr.v44i01a05","DOI":"10.14745\/ccdr.v44i01a05"},{"key":"key-10.3934\/mbe.2023778-10","doi-asserted-by":"publisher","unstructured":"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., <b>23<\/b> (2017), 1223\u20131225. https:\/\/doi.org\/10.3201\/eid2307.170519","DOI":"10.3201\/eid2307.170519"},{"key":"key-10.3934\/mbe.2023778-11","doi-asserted-by":"publisher","unstructured":"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, <i>Travel Med. Infect. Dis<\/i>., <b>21<\/b> (2018), 56\u201361. https:\/\/doi.org\/10.1016\/j.tmaid.2017.11.012","DOI":"10.1016\/j.tmaid.2017.11.012"},{"key":"key-10.3934\/mbe.2023778-12","doi-asserted-by":"publisher","unstructured":"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, <i>Acta Trop<\/i>., <b>199<\/b> (2019), 1\u20136. https:\/\/doi.org\/10.1016\/j.actatropica.2019.105114","DOI":"10.1016\/j.actatropica.2019.105114"},{"key":"key-10.3934\/mbe.2023778-13","unstructured":"<i>International Travel Health Advisory Network<\/i>, 2022. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.ithc.cn\/article\/460057.html\">https:\/\/www.ithc.cn\/article\/460057.html<\/ext-link>."},{"key":"key-10.3934\/mbe.2023778-14","unstructured":"<i>World Health Organization<\/i>, Zika virus, 2018. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.who.int\/mediacentre\/factsheets\/zika\/en\/\">https:\/\/www.who.int\/mediacentre\/factsheets\/zika\/en\/<\/ext-link>."},{"key":"key-10.3934\/mbe.2023778-15","doi-asserted-by":"publisher","unstructured":"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, <i>Clin. Infect. Dis.<\/i>, <b>64<\/b> (2017), 211\u2013213. https:\/\/doi.org\/10.1093\/cid\/ciw692","DOI":"10.1093\/cid\/ciw692"},{"key":"key-10.3934\/mbe.2023778-16","doi-asserted-by":"publisher","unstructured":"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, <i>MMWR-Morbid. Mortal. W.<\/i>, <b>65<\/b> (2016), 371\u2013374. http:\/\/dx.doi.org\/10.15585\/mmwr.mm6514a3","DOI":"10.15585\/mmwr.mm6514a3"},{"key":"key-10.3934\/mbe.2023778-17","doi-asserted-by":"publisher","unstructured":"S. Thangamani, J. Huang, C. E. Hart, H. Guzman, R. B. Tesh, Vertical transmission of Zika virus in Aedes aegypti mosquitoes, <i>Am. J. Trop. Med. Hyg.<\/i>, <b>95<\/b> (2016), 1169\u20131173. https:\/\/doi.org\/10.4269\/ajtmh.16-0448","DOI":"10.4269\/ajtmh.16-0448"},{"key":"key-10.3934\/mbe.2023778-18","doi-asserted-by":"publisher","unstructured":"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, <i>Nat. Commun.<\/i>, <b>10<\/b> (2019), 1\u201311. https:\/\/doi.org\/10.1038\/s41467-019-09256-0","DOI":"10.1038\/s41467-019-09256-0"},{"key":"key-10.3934\/mbe.2023778-19","doi-asserted-by":"crossref","unstructured":"Microcephaly Epidemic Research Group, Microcephaly in infants, Pernambuco state, Brazil, 2015, <i>Emerg. Infect. Dis.<\/i>, <b>22<\/b> (2016), 1090\u20131093. <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/doi.org\/10.3201\/eid2206.160062\">https:\/\/doi.org\/10.3201\/eid2206.160062<\/ext-link>","DOI":"10.3201\/eid2206.160062"},{"key":"key-10.3934\/mbe.2023778-20","doi-asserted-by":"publisher","unstructured":"L. S. Munoz, P. Barreras, C. A. Pardo, Zika virus-associated neurological disease in the adult: Guillain-Barr\u00e9 syndrome, encephalitis, and myelitis, <i>Semin. Reprod. Med.<\/i>, <b>34<\/b> (2016), 273\u2013279. https:\/\/dx.doi.org\/10.1055\/s-0036-1592066","DOI":"10.1055\/s-0036-1592066"},{"key":"key-10.3934\/mbe.2023778-21","doi-asserted-by":"crossref","unstructured":"F. Brauer, C. Castillo-Chavez, <i>Mathematical models in population biology and epidemiology<\/i>, Springer Press, 2001.","DOI":"10.1007\/978-1-4757-3516-1"},{"key":"key-10.3934\/mbe.2023778-22","doi-asserted-by":"publisher","unstructured":"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, <i>Sci. Rep.<\/i>, <b>6<\/b> (2016), 1\u20136. https:\/\/doi.org\/10.1038\/srep28070","DOI":"10.1038\/srep28070"},{"key":"key-10.3934\/mbe.2023778-23","doi-asserted-by":"publisher","unstructured":"F. B. Agusto, S. Bewick, W. F. Fagan, Mathematical model of zika virus with vertical transmission, <i>Infec. Dis. Model<\/i>, <b>2<\/b> (2017), 244\u2013267. https:\/\/doi.org\/10.1016\/j.idm.2017.05.003","DOI":"10.1016\/j.idm.2017.05.003"},{"key":"key-10.3934\/mbe.2023778-24","doi-asserted-by":"publisher","unstructured":"H. Zhao, L. Wang, S. M. Oliva, H. Zhu, Modeling and dynamics analysis of Zika transmission with limited medical resources, <i>B. Math. Biol.<\/i>, <b>82<\/b> (2020), 99. https:\/\/doi.org\/10.1007\/s11538-020-00776-1","DOI":"10.1007\/s11538-020-00776-1"},{"key":"key-10.3934\/mbe.2023778-25","doi-asserted-by":"publisher","unstructured":"L. Wang, H. Zhao, S. M. Oliva, H. Zhu, Modeling the transmission and control of Zika in Brazil, <i>Sci. Rep-UK<\/i>, <b>7<\/b> (2017), 7721. https:\/\/doi.org\/10.1038\/s41598-017-07264-y","DOI":"10.1038\/s41598-017-07264-y"},{"key":"key-10.3934\/mbe.2023778-26","doi-asserted-by":"publisher","unstructured":"X. Yuan, Y. Lou, D. He, J. Wang, D. Gao, A Zika Endemic Model for the Contribution of Multiple Transmission Routes, <i>B. Math. Biol.<\/i>, <b>83<\/b> (2021), 111. https:\/\/doi.org\/10.1007\/s11538-021-00945-w","DOI":"10.1007\/s11538-021-00945-w"},{"key":"key-10.3934\/mbe.2023778-27","doi-asserted-by":"publisher","unstructured":"L. Wang, H. Zhao, Modeling and dynamics analysis of Zika transmission with contaminated aquatic environments, <i>Nonlinear Dynam.<\/i>, <b>104<\/b> (2021), 845\u2013862. https:\/\/doi.org\/10.1007\/s11071-021-06289-3","DOI":"10.1007\/s11071-021-06289-3"},{"key":"key-10.3934\/mbe.2023778-28","doi-asserted-by":"publisher","unstructured":"W. Fitzgibbon, J. Morgan, G. Webb, An outbreak vector-host epidemic model with spatial structure: the 2015\u20132016 Zika outbreak in Rio De Janeiro, <i>Theor. Biol. Med. Model<\/i>, <b>14<\/b> (2017), 7. https:\/\/doi.org\/10.1186\/s12976-017-0051-z","DOI":"10.1186\/s12976-017-0051-z"},{"key":"key-10.3934\/mbe.2023778-29","doi-asserted-by":"publisher","unstructured":"Y. Cai, K. Wang, W. Wang, Global transmission dynamics of a Zika virus model, <i>Appl. Math. Lett.<\/i>, <b>92<\/b> (2019), 190\u2013195. https:\/\/doi.org\/10.1016\/j.aml.2019.01.015","DOI":"10.1016\/j.aml.2019.01.015"},{"key":"key-10.3934\/mbe.2023778-30","doi-asserted-by":"publisher","unstructured":"F. Li, X. Zhao, Global dynamics of a reaction\u2013diffusion model of Zika virus transmission with seasonality, <i>B. Math. Biol.<\/i>, <b>83<\/b> (2021), 43. https:\/\/doi.org\/10.1007\/s11538-021-00879-3","DOI":"10.1007\/s11538-021-00879-3"},{"key":"key-10.3934\/mbe.2023778-31","doi-asserted-by":"publisher","unstructured":"Y. Zhao, D. Jiang, The threshold of a stochastic SIS epidemic model with vaccination, <i>Appl. Math. Comput.<\/i>, <b>243<\/b> (2014), 718\u2013727. https:\/\/doi.org\/10.1016\/j.amc.2014.05.124","DOI":"10.1016\/j.amc.2014.05.124"},{"key":"key-10.3934\/mbe.2023778-32","doi-asserted-by":"publisher","unstructured":"Z. Shi, X. Zhang, D. Jiang, Dynamics of an avian influenza model with half-saturated incidence, <i>Appl. Math. Comput.<\/i>, <b>355<\/b> (2019), 399\u2013416. https:\/\/doi.org\/10.1016\/j.amc.2019.02.070","DOI":"10.1016\/j.amc.2019.02.070"},{"key":"key-10.3934\/mbe.2023778-33","doi-asserted-by":"publisher","unstructured":"L. Xue, X. Cao, H. Wan, Releasing Wolbachia-infected mosquitos to mitigate the transmission of Zika virus, <i>J. Math. Anal. Appl.<\/i>, <b>496<\/b> (2021), 124804 https:\/\/doi.org\/10.1016\/j.jmaa.2020.124804","DOI":"10.1016\/j.jmaa.2020.124804"},{"key":"key-10.3934\/mbe.2023778-34","doi-asserted-by":"publisher","unstructured":"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, <i>Appl. Math. Comput.<\/i>, <b>394<\/b> (2021), 125798. https:\/\/doi.org\/10.1016\/j.amc.2020.125798","DOI":"10.1016\/j.amc.2020.125798"},{"key":"key-10.3934\/mbe.2023778-35","doi-asserted-by":"publisher","unstructured":"T. Y. Miyaoka, S. Lenhart, J. F. C. A. Meyer, Optimal control of vaccination in a vector-borne reaction\u2013diffusion model applied to Zika virus, <i>J. Math. Biol.<\/i>, <b>79<\/b> (2019), 1077\u20131104. https:\/\/doi.org\/10.1007\/s00285-019-01390-z","DOI":"10.1007\/s00285-019-01390-z"},{"key":"key-10.3934\/mbe.2023778-36","doi-asserted-by":"publisher","unstructured":"E. Bonyah, M. A. Khan, K. O. Okosun, S. Islam, A theoretical model for Zika virus transmission, <i>Plos One<\/i>, <b>12<\/b> (2017), e0185540. https:\/\/doi.org\/10.1371\/journal.pone.0185540","DOI":"10.1371\/journal.pone.0185540"},{"key":"key-10.3934\/mbe.2023778-37","doi-asserted-by":"publisher","unstructured":"M. A. Khan, S. W. Shah, S. Ullah, J. F. G\u00f3mez-Aguilar, A dynamical model of asymptomatic carrier zika virus with optimal control strategies, <i>Nonlinear Anal-Real.<\/i>, <b>50<\/b> (2019), 144\u2013170. https:\/\/doi.org\/10.1016\/j.nonrwa.2019.04.006","DOI":"10.1016\/j.nonrwa.2019.04.006"},{"key":"key-10.3934\/mbe.2023778-38","doi-asserted-by":"publisher","unstructured":"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, <i>J. Theor. Biol.<\/i>, <b>356<\/b> (2014), 174\u2013191. https:\/\/doi.org\/10.1016\/j.jtbi.2014.04.033","DOI":"10.1016\/j.jtbi.2014.04.033"},{"key":"key-10.3934\/mbe.2023778-39","doi-asserted-by":"publisher","unstructured":"L. Xue, X. Fang, J. M. Hyman, Comparing the effectiveness of different strains of Wolbachia for controlling chikungunya, dengue fever, and zika, <i>PLos. Negl. Trop. Dis.<\/i>, <b>12<\/b> (2018), e0006666. https:\/\/doi.org\/10.1371\/journal.pntd.0006666","DOI":"10.1371\/journal.pntd.0006666"},{"key":"key-10.3934\/mbe.2023778-40","doi-asserted-by":"publisher","unstructured":"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, <i>Eurosurveillance<\/i>, <b>19<\/b> (2014), 20751. https:\/\/doi.org\/10.2807\/1560-7917.ES2014.19.13.20751","DOI":"10.2807\/1560-7917.ES2014.19.13.20751"},{"key":"key-10.3934\/mbe.2023778-41","doi-asserted-by":"publisher","unstructured":"C. Bowman, A. B. Gumel, P. van den Driessche, J. Wu, H. Zhu, A mathematical model for assessing control strategies against West Nile virus, <i>B. Math. Biol.<\/i>, <b>67<\/b> (2005), 1107\u20131133. https:\/\/doi.org\/10.1016\/j.bulm.2005.01.002","DOI":"10.1016\/j.bulm.2005.01.002"},{"key":"key-10.3934\/mbe.2023778-42","doi-asserted-by":"publisher","unstructured":"M. Andraud, N. Hens, C. Marais, P. Beutels, Dynamic epidemiological models for dengue transmission: a systematic review of structural approaches, <i>Plos One<\/i>, <b>7<\/b> (2012), e49085. https:\/\/doi.org\/10.1371\/journal.pone.0049085","DOI":"10.1371\/journal.pone.0049085"},{"key":"key-10.3934\/mbe.2023778-43","doi-asserted-by":"publisher","unstructured":"E. Chikaki, H. Ishikawa, A dengue transmission model in Tailand considering sequential infections with all four serotypes, <i>J. Infect. Dev. Countr.<\/i>, <b>3<\/b> (2009), 711\u2013722. https:\/\/doi.org\/10.3855\/jidc.616","DOI":"10.3855\/jidc.616"},{"key":"key-10.3934\/mbe.2023778-44","unstructured":"X. Mao, <i>Stochastic differential equations and applications<\/i>, second edition, Horwood Press, Chichester, 2007."},{"key":"key-10.3934\/mbe.2023778-45","doi-asserted-by":"publisher","unstructured":"K. Liu, Stationary distributions of second order stochastic evolution equations with memory in Hilbert spaces, <i>Stoch. Proc. Appl.<\/i>, <b>130<\/b> (2020), 366\u2013393. https:\/\/doi.org\/10.1016\/j.spa.2019.03.015","DOI":"10.1016\/j.spa.2019.03.015"},{"key":"key-10.3934\/mbe.2023778-46","unstructured":"R. M. Dudley, <i>Real Analysis and Probability<\/i>, second edition, Cambridge University Press, 2003."},{"key":"key-10.3934\/mbe.2023778-47","doi-asserted-by":"publisher","unstructured":"H. J. Kushner, Existence results for optimal stochastic controls, <i>J. Optim. Theory. Appl.<\/i>, <b>15<\/b> (1975), 347\u2013359. https:\/\/doi.org\/10.1007\/BF00933203","DOI":"10.1007\/BF00933203"},{"key":"key-10.3934\/mbe.2023778-48","unstructured":"J. Yong, X. Zhou, <i>Stochastic Control: Hamiltonian Systems and HJB Equations<\/i>, Springer Press, 1999."},{"key":"key-10.3934\/mbe.2023778-49","doi-asserted-by":"publisher","unstructured":"D. J. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations, <i>SIAM Rev.<\/i>, <b>43<\/b> (2001), 525\u2013546. https:\/\/doi.org\/10.1137\/s0036144500378302","DOI":"10.1137\/s0036144500378302"},{"key":"key-10.3934\/mbe.2023778-50","doi-asserted-by":"publisher","unstructured":"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, <i>Parasite. Vector.<\/i>, <b>6<\/b> (2013), 351. https:\/\/doi.org\/10.1186\/1756-3305-6-351","DOI":"10.1186\/1756-3305-6-351"}],"container-title":["Mathematical Biosciences and Engineering"],"original-title":[],"link":[{"URL":"http:\/\/www.aimspress.com\/article\/doi\/10.3934\/mbe.2023778?viewType=html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T06:50:37Z","timestamp":1694760637000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.aimspress.com\/article\/doi\/10.3934\/mbe.2023778"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"references-count":50,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2023]]}},"URL":"https:\/\/doi.org\/10.3934\/mbe.2023778","relation":{},"ISSN":["1551-0018"],"issn-type":[{"value":"1551-0018","type":"print"}],"subject":[],"published":{"date-parts":[[2023]]}}}