{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T01:30:06Z","timestamp":1789522206217,"version":"build-2803163510"},"reference-count":59,"publisher":"AIP Publishing","issue":"3","funder":[{"DOI":"10.13039\/501100001412","name":"Council of Scientific and Industrial Research, India","doi-asserted-by":"publisher","award":["25(0303)\/19\/EMR-II"],"award-info":[{"award-number":["25(0303)\/19\/EMR-II"]}],"id":[{"id":"10.13039\/501100001412","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2024,3,1]]},"abstract":"<jats:p>Viral infections spread by mosquitoes are a growing threat to human health and welfare. Zika virus (ZIKV) is one of them and has become a global worry, particularly for women who are pregnant. To study ZIKV dynamics in the presence of demographic stochasticity, we consider an established ZIKV transmission model that takes into consideration the disease transmission from human to mosquito, mosquito to human, and human to human. In this study, we look at the local stability of the disease-free and endemic equilibriums. By conducting the sensitivity analysis both locally and globally, we assess the effect of the model parameters on the model outcomes. In this work, we use the continuous-time Markov chain (CTMC) process to develop and analyze a stochastic model. The main distinction between deterministic and stochastic models is that, in the absence of any preventive measures such as avoiding travel to infected areas, being careful from mosquito bites, taking precautions to reduce the risk of sexual transmission, and seeking medical care for any acute illness with a rash or fever, the stochastic model shows the possibility of disease extinction in a finite amount of time, unlike the deterministic model shows disease persistence. We found that the numerically estimated disease extinction probability agrees well with the analytical probability obtained from the Galton\u2013Watson branching process approximation. We have discovered that the disease extinction probability is high if the disease emerges from infected mosquitoes rather than infected humans. In the context of the stochastic model, we derive the implicit equation of the mean first passage time, which computes the average amount of time needed for a system to undergo its first state transition.<\/jats:p>","DOI":"10.1063\/5.0190996","type":"journal-article","created":{"date-parts":[[2024,3,15]],"date-time":"2024-03-15T21:48:48Z","timestamp":1710539328000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":4,"title":["The effect of demographic stochasticity on Zika virus transmission dynamics: Probability of disease extinction, sensitivity analysis, and mean first passage time"],"prefix":"10.1063","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-3601-3104","authenticated-orcid":false,"given":"Sunil","family":"Maity","sequence":"first","affiliation":[{"name":"Department of Mathematics, NIT Patna , Patna 800005, Bihar, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2549-5444","authenticated-orcid":false,"given":"Partha","family":"Sarathi Mandal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, NIT Patna , Patna 800005, Bihar, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2024,3,15]]},"reference":[{"key":"2024031521484224600_c1","doi-asserted-by":"publisher","first-page":"28070","DOI":"10.1038\/srep28070","article-title":"Prevention and control of Zika as a mosquito-borne and sexually transmitted disease: A mathematical modeling analysis","volume":"6","year":"2016","journal-title":"Sci. Rep."},{"key":"2024031521484224600_c2","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1016\/j.apjtm.2017.03.020","article-title":"Advances in research on Zika virus","volume":"10","year":"2017","journal-title":"Asian Pac. J. Trop. Med."},{"key":"2024031521484224600_c3","doi-asserted-by":"publisher","first-page":"723","DOI":"10.1016\/j.apjtm.2016.06.019","article-title":"Zika: As an emergent epidemic","volume":"9","year":"2016","journal-title":"Asian Pac. J. Trop. Med."},{"key":"2024031521484224600_c4"},{"key":"2024031521484224600_c5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.9734\/BJMCS\/2016\/29834","article-title":"Stability analysis of deterministic mathematical model for Zika virus","volume":"19","year":"2016","journal-title":"Br. J. Math. Comput. Sci."},{"key":"2024031521484224600_c6"},{"key":"2024031521484224600_c7","doi-asserted-by":"publisher","first-page":"e1009068","DOI":"10.1371\/journal.ppat.1009068","article-title":"Modeling intra-mosquito dynamics of Zika virus and its dose-dependence confirms the low epidemic potential of Aedes albopictus","volume":"16","year":"2020","journal-title":"PLoS Pathog."},{"key":"2024031521484224600_c8","doi-asserted-by":"publisher","first-page":"e2681","DOI":"10.1371\/journal.pntd.0002681","article-title":"Zika virus in gabon (Central Africa)\u20132007: A new threat from Aedes albopictus?","volume":"8","year":"2014","journal-title":"PLoS Neglected Trop. Dis."},{"key":"2024031521484224600_c9","doi-asserted-by":"publisher","first-page":"2536","DOI":"10.1056\/NEJMoa0805715","article-title":"Zika virus outbreak on Yap Island, federated states of Micronesia","volume":"360","year":"2009","journal-title":"N. Engl. J. Med."},{"key":"2024031521484224600_c10","doi-asserted-by":"publisher","first-page":"37","DOI":"10.4103\/0972-9062.331411","article-title":"Zika virus vertical transmission in mosquitoes: A less understood mechanism","volume":"59","year":"2022","journal-title":"J. Vector Borne Dis."},{"key":"2024031521484224600_c11","doi-asserted-by":"publisher","first-page":"e0004726","DOI":"10.1371\/journal.pntd.0004726","article-title":"Transmission dynamics of Zika virus in island populations: A modelling analysis of the 2013\u201314 French Polynesia outbreak","volume":"10","year":"2016","journal-title":"PLoS Neglected Trop. Dis."},{"key":"2024031521484224600_c12","doi-asserted-by":"publisher","first-page":"e0185540","DOI":"10.1371\/journal.pone.0185540","article-title":"A theoretical model for Zika virus transmission","volume":"12","year":"2017","journal-title":"PLoS One"},{"key":"2024031521484224600_c13","doi-asserted-by":"publisher","first-page":"105532","DOI":"10.1016\/j.cnsns.2020.105532","article-title":"Optimal control strategies of Zika virus model with mutant","volume":"93","year":"2021","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"2024031521484224600_c14","doi-asserted-by":"publisher","first-page":"111137","DOI":"10.1016\/j.chaos.2021.111137","article-title":"Modeling assumptions, optimal control strategies and mitigation through vaccination to Zika virus","volume":"150","year":"2021","journal-title":"Chaos, Solitons Fractals"},{"key":"2024031521484224600_c15","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1186\/s13662-020-03044-7","article-title":"A new mathematical model for Zika virus transmission","volume":"2020","journal-title":"Adv. Differ. Equ."},{"key":"2024031521484224600_c16","doi-asserted-by":"publisher","first-page":"244","DOI":"10.1016\/j.idm.2017.05.003","article-title":"Mathematical model of Zika virus with vertical transmission","volume":"2","year":"2017","journal-title":"Infect. Dis. Model."},{"key":"2024031521484224600_c17","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1016\/j.matcom.2019.04.007","article-title":"Mathematical modelling of Zika virus as a mosquito-borne and sexually transmitted disease with diffusion effects","volume":"166","year":"2019","journal-title":"Math. Comput. Simul."},{"key":"2024031521484224600_c18","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1016\/j.epidem.2017.06.003","article-title":"Zika virus dynamics: When does sexual transmission matter?","volume":"21","year":"2017","journal-title":"Epidemics"},{"key":"2024031521484224600_c19"},{"key":"2024031521484224600_c20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11538-022-01001-x","article-title":"A comparison of deterministic and stochastic plant-vector-virus models based on probability of disease extinction and outbreak","volume":"84","year":"2022","journal-title":"Bull. Math. Biol."},{"key":"2024031521484224600_c21","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/s10441-020-09391-y","article-title":"Probability of disease extinction or outbreak in a stochastic epidemic model for west nile virus dynamics in birds","volume":"69","year":"2021","journal-title":"Acta Biotheor."},{"key":"2024031521484224600_c22","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1016\/j.idm.2017.03.001","article-title":"A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis","volume":"2","year":"2017","journal-title":"Infect. Dis. Model."},{"key":"2024031521484224600_c23","doi-asserted-by":"publisher","first-page":"6185","DOI":"10.1016\/j.idm.2017.03.001","article-title":"Stochastic mathematical models in epidemiology","volume":"20","year":"2017","journal-title":"Information"},{"key":"2024031521484224600_c24","doi-asserted-by":"publisher","first-page":"1583","DOI":"10.1016\/j.apm.2013.08.031","article-title":"Stochastic modeling of phytoplankton allelopathy","volume":"38","year":"2014","journal-title":"Appl. Math. Model."},{"key":"2024031521484224600_c25"},{"key":"2024031521484224600_c26","doi-asserted-by":"publisher","first-page":"020023","DOI":"10.1063\/1.5026095","article-title":"Deterministic and stochastic CTMC models from Zika disease transmission","volume":"1937","year":"2018","journal-title":"AIP Conf. Proc."},{"key":"2024031521484224600_c27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13662-021-03308-w","article-title":"On the effect of postponing pregnancy in a Zika transmission model","volume":"2021","year":"2021","journal-title":"Adv. Differ. Equ."},{"key":"2024031521484224600_c28","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/S0025-5564(98)10003-2","article-title":"Analysis of a dengue disease transmission model","volume":"150","year":"1998","journal-title":"Math. Biosci."},{"key":"2024031521484224600_c29"},{"key":"2024031521484224600_c30","doi-asserted-by":"publisher","first-page":"110864","DOI":"10.1016\/j.chaos.2021.110864","article-title":"Optimal control strategies of a fractional order model for Zika virus infection involving various transmissions","volume":"146","year":"2021","journal-title":"Chaos, Solitons Fractals"},{"key":"2024031521484224600_c31","doi-asserted-by":"publisher","first-page":"615","DOI":"10.4314\/jasem.v21i4.1","article-title":"A mathematical model for the dynamics of Zika virus via homotopy perturbation method","volume":"21","year":"2017","journal-title":"J. Appl. Sci. Environ. Manag."},{"key":"2024031521484224600_c32","doi-asserted-by":"publisher","first-page":"117","DOI":"10.22034\/cmde.2019.34715.1585","article-title":"A mathematical analysis of Zika virus transmission with optimal control strategies","volume":"9","year":"2021","journal-title":"Comput. Methods Differ. Equ."},{"key":"2024031521484224600_c33","doi-asserted-by":"publisher","first-page":"4429","DOI":"10.3934\/dcdsb.2021235","article-title":"A mathematical model for biodiversity diluting transmission of Zika virus through competition mechanics","volume":"27","year":"2021","journal-title":"Discrete Contin. Dyn. Syst.-B"},{"key":"2024031521484224600_c34","volume-title":"Mathematics in Population Biology","year":"2018"},{"key":"2024031521484224600_c35"},{"key":"2024031521484224600_c36","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1051\/proc\/201862123","article-title":"An introduction to the basic reproduction number in mathematical epidemiology","volume":"62","year":"2018","journal-title":"ESAIM: Proc. Surv."},{"key":"2024031521484224600_c37","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","article-title":"Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission","volume":"180","year":"2002","journal-title":"Math. Biosci."},{"key":"2024031521484224600_c38","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/BF00178324","article-title":"On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations","volume":"28","year":"1990","journal-title":"J. Math. Biol."},{"key":"2024031521484224600_c39","doi-asserted-by":"publisher","first-page":"873","DOI":"10.1098\/rsif.2009.0386","article-title":"The construction of next-generation matrices for compartmental epidemic models","volume":"7","year":"2010","journal-title":"J. R. Soc. Interface"},{"key":"2024031521484224600_c40","doi-asserted-by":"publisher","first-page":"2289","DOI":"10.3390\/math10132289","article-title":"Quiescence generates moving average in a stochastic epidemiological model with one host and two parasites","volume":"10","year":"2022","journal-title":"Mathematics"},{"key":"2024031521484224600_c41","volume-title":"Topics in Mathematical Biology","year":"2017"},{"key":"2024031521484224600_c42","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1038\/336239a0","article-title":"Rate of evolution slowed by a dormant propagule pool","volume":"336","year":"1988","journal-title":"Nature"},{"key":"2024031521484224600_c43","volume-title":"Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review","year":"2000"},{"key":"2024031521484224600_c44","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1016\/j.jtbi.2008.04.011","article-title":"A methodology for performing global uncertainty and sensitivity analysis in systems biology","volume":"254","year":"2008","journal-title":"J. Theor. Biol."},{"key":"2024031521484224600_c45","doi-asserted-by":"publisher","first-page":"229","DOI":"10.2307\/1403510","article-title":"Sensitivity and uncertainty analysis of complex models of disease transmission: An HIV model, as an example","volume":"62","year":"1994","journal-title":"Int. Stat. Rev.\/Revue Internationale de Statistique"},{"key":"2024031521484224600_c46","volume-title":"An Introduction to Stochastic Processes with Applications to Biology","year":"2010"},{"key":"2024031521484224600_c47"},{"key":"2024031521484224600_c48","doi-asserted-by":"publisher","first-page":"590","DOI":"10.1080\/17513758.2012.665502","article-title":"Extinction thresholds in deterministic and stochastic epidemic models","volume":"6","year":"2012","journal-title":"J. Biol. Dyn."},{"key":"2024031521484224600_c49","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1016\/j.mbs.2013.02.006","article-title":"Relations between deterministic and stochastic thresholds for disease extinction in continuous-and discrete-time infectious disease models","volume":"243","year":"2013","journal-title":"Math. Biosci."},{"key":"2024031521484224600_c50"},{"key":"2024031521484224600_c51"},{"key":"2024031521484224600_c52","doi-asserted-by":"publisher","first-page":"083120","DOI":"10.1063\/5.0096638","article-title":"Impact of demographic variability on the disease dynamics for honeybee model","volume":"32","year":"2022","journal-title":"Chaos"},{"key":"2024031521484224600_c53","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/j.tpb.2019.04.004","article-title":"A stochastic epidemic model for the dynamics of two pathogens in a single tick population","volume":"127","year":"2019","journal-title":"Theor. Popul. Biol."},{"key":"2024031521484224600_c54","doi-asserted-by":"publisher","first-page":"1999","DOI":"10.1007\/s11538-017-0317-y","article-title":"A stochastic tick-borne disease model: Exploring the probability of pathogen persistence","volume":"79","year":"2017","journal-title":"Bull. Math. Biol."},{"key":"2024031521484224600_c55","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.1007\/s11538-013-9848-z","article-title":"Probability of a disease outbreak in stochastic multipatch epidemic models","volume":"75","year":"2013","journal-title":"Bull. Math. Biol."},{"key":"2024031521484224600_c56","doi-asserted-by":"publisher","first-page":"851","DOI":"10.1098\/rsif.2007.1064","article-title":"Stochasticity and heterogeneity in host\u2013vector models","volume":"4","year":"2007","journal-title":"J. R. Soc. Interface"},{"key":"2024031521484224600_c57"},{"key":"2024031521484224600_c58","volume-title":"Introduction to Modeling and Analysis of Stochastic Systems","year":"2011"},{"key":"2024031521484224600_c59","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1016\/0021-9991(76)90041-3","article-title":"A general method for numerically simulating the stochastic time evolution of coupled chemical reactions","volume":"22","year":"1976","journal-title":"J. Comput. Phys."}],"container-title":["Chaos: An Interdisciplinary Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/5.0190996\/19797274\/033126_1_5.0190996.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/5.0190996\/19797274\/033126_1_5.0190996.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,15]],"date-time":"2024-03-15T21:48:56Z","timestamp":1710539336000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/cha\/article\/34\/3\/033126\/3275682\/The-effect-of-demographic-stochasticity-on-Zika"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,1]]},"references-count":59,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,3,1]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0190996","relation":{},"ISSN":["1054-1500","1089-7682"],"issn-type":[{"value":"1054-1500","type":"print"},{"value":"1089-7682","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2024,3]]},"published":{"date-parts":[[2024,3,1]]},"article-number":"033126"}}