{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:34:34Z","timestamp":1760146474840,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,11,11]],"date-time":"2024-11-11T00:00:00Z","timestamp":1731283200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Informatics"],"abstract":"<jats:p>In this research, we formulated a fractional-order model for the transmission dynamics of Zika virus, incorporating three control strategies: health education campaigns, the use of insecticides, and preventive measures. We conducted a theoretical analysis of the model, obtaining the disease-free equilibrium and the basic reproduction number, and analyzing the existence and uniqueness of the model. Additionally, we performed model parameter estimation using real data on Zika virus cases reported in Colombia. We found that the fractional-order model provided a better fit to the real data compared to the classical integer-order model. A sensitivity analysis of the basic reproduction number was conducted using computed partial rank correlation coefficients to assess the impact of each parameter on Zika virus transmission. Furthermore, we performed numerical simulations to determine the effect of memory on the spread of Zika virus. The simulation results showed that the order of derivatives significantly impacts the dynamics of the disease. We also assessed the effect of the control strategies through simulations, concluding that the proposed interventions have the potential to significantly reduce the spread of Zika virus in the population.<\/jats:p>","DOI":"10.3390\/informatics11040085","type":"journal-article","created":{"date-parts":[[2024,11,12]],"date-time":"2024-11-12T06:28:32Z","timestamp":1731392912000},"page":"85","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Modeling Zika Virus Disease Dynamics with Control Strategies"],"prefix":"10.3390","volume":"11","author":[{"given":"Mlyashimbi","family":"Helikumi","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science and Technical Education, Mbeya University of Science and Technology, Mbeya P.O. Box 131, Tanzania"}]},{"given":"Paride O.","family":"Lolika","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Juba, Juba P.O. Box 82, Central Equatoria, South Sudan"}]},{"given":"Kimulu Ancent","family":"Makau","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Machakos University, Machakos P.O. Box 136-90100, Kenya"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0391-2577","authenticated-orcid":false,"given":"Muli Charles","family":"Ndambuki","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Machakos University, Machakos P.O. Box 136-90100, Kenya"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6481-6840","authenticated-orcid":false,"given":"Adquate","family":"Mhlanga","sequence":"additional","affiliation":[{"name":"The Program for Experimental and Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Chicago, Maywood, IL 84101, USA"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhu, J., Khan, F., Khan, S.U., Sumelka, W., Khan, F.U., and AlQahtani, S.A. (2024). Computational investigation of stochastic Zika virus optimal control model using Legendre spectral method. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-69096-x"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"145","DOI":"10.22436\/jmcs.028.02.03","article-title":"Caputo fractional order derivative model of Zika virus transmission dynamics","volume":"28","author":"Prasad","year":"2023","journal-title":"J. Math. Comput. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Kouidere, A., El Bhih, A., Minifi, I., Balatif, O., and Adnaoui, K. (2024). Optimal control problem for mathematical modeling of Zika virus transmission using fractional order derivatives. Front. Appl. Math. Stat., 10.","DOI":"10.3389\/fams.2024.1376507"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"20180795","DOI":"10.1098\/rspb.2018.0795","article-title":"Temperature drives Zika virus transmission: Evidence from empirical and mathematical models","volume":"285","author":"Tesla","year":"2018","journal-title":"Proc. R. Soc. B"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1063\/5.0190996","article-title":"The effect of demographic stochasticity on Zika virus transmission dynamics: Probability of disease extinction, sensitivity analysis, and mean first passage time","volume":"34","author":"Maity","year":"2024","journal-title":"Chaos Interdiscip. J. Nonlinear Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.jneuroim.2017.03.001","article-title":"Zika virus: History, epidemiology, transmission, and clinical presentation","volume":"308","author":"Song","year":"2017","journal-title":"J. Neuroimmunol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"6350134","DOI":"10.1155\/2020\/6350134","article-title":"Modeling the control of Zika virus vector population using the sterile insect technology","volume":"2020","author":"Atokolo","year":"2020","journal-title":"J. Appl. Math."},{"key":"ref_8","first-page":"1","article-title":"Estimation of Zika virus prevalence by appearance of microcephaly","volume":"16","author":"Ma","year":"2016","journal-title":"BMC Infect. Dis."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.matcom.2019.02.009","article-title":"Mathematical modeling and numerical simulations of Zika in Colombia considering mutation","volume":"163","author":"Benincasa","year":"2019","journal-title":"Math. Comput. Simul."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"82","DOI":"10.9734\/arjom\/2022\/v18i930409","article-title":"Global dynamics of fractional-order model for malaria disease transmission","volume":"18","author":"Helikumi","year":"2022","journal-title":"Asian Res. J. Math."},{"key":"ref_11","first-page":"6","article-title":"Numerical Investigation of HIV\/AIDS Dynamics Among the Truckers and the Local Community at Malaba and Busia Border Stops","volume":"13","author":"Kimulu","year":"2023","journal-title":"Am. J. Comput. Appl. Math."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"50","DOI":"10.48185\/jmam.v3i1.424","article-title":"Male circumcision: A means to reduce HIV transmission between truckers and female sex workers in Kenya","volume":"3","author":"Kimulu","year":"2022","journal-title":"J. Math. Anal. Model."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"123516","DOI":"10.1016\/j.physa.2019.123516","article-title":"A new application of fractional Atangana\u2013Baleanu derivatives: Designing ABC-fractional masks in image processing","volume":"542","author":"Ghanbari","year":"2020","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_14","first-page":"4178073","article-title":"A Fractional-Order Model for Zika Virus Infection with Multiple Delays","volume":"1","author":"Rakkiyappan","year":"2019","journal-title":"Wiley Online Libr."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"100276","DOI":"10.1016\/j.health.2023.100276","article-title":"A non-integer order model for Zika and Dengue co-dynamics with cross-enhancement","volume":"4","author":"Iheonu","year":"2023","journal-title":"Healthc. Anal."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.orhc.2017.08.004","article-title":"Optimal control of intervention strategies and cost effectiveness analysis for a Zika virus model","volume":"18","author":"Momoh","year":"2018","journal-title":"Oper. Res. Health Care"},{"key":"ref_17","first-page":"5118382","article-title":"Dynamics of a Fractional-Order Chikungunya Model with Asymptomatic Infectious Class","volume":"1","author":"Helikumi","year":"2022","journal-title":"Comput. Math. Methods Med."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.aej.2024.03.059","article-title":"A review of fractional order epidemic models for life sciences problems: Past, present and future","volume":"95","author":"Nisar","year":"2024","journal-title":"Alex. Eng. J."},{"key":"ref_19","doi-asserted-by":"crossref","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","author":"Sharma","year":"2021","journal-title":"Chaos Solitons Fractals"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Gizaw, A.K., and Deressa, C.T. (2024). Fractional-order analysis of temperature- and rainfall-dependent mathematical model for malaria transmission dynamics. Front. Appl. Math. Stat., 10.","DOI":"10.3389\/fams.2024.1396650"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1186\/s13662-021-03532-4","article-title":"Modeling, analysis and numerical solution to malaria fractional model with temporary immunity and relapse","volume":"2021","author":"Singh","year":"2021","journal-title":"Adv. Differ. Equs."},{"key":"ref_22","first-page":"6652037","article-title":"Modeling and Analysis of an Age-Structured Malaria Model in the Sense of Atangana\u2013Baleanu Fractional Operators","volume":"2024","author":"Menbiko","year":"2024","journal-title":"J. Appl. Math."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"100210","DOI":"10.1016\/j.health.2023.100210","article-title":"A fractional-order mathematical model for malaria and COVID-19 co-infection dynamics","volume":"4","author":"Abioye","year":"2023","journal-title":"Healthc. Anal."},{"key":"ref_24","first-page":"132","article-title":"A fractional order co-infection model between malaria and filariasis epidemic","volume":"31","author":"Kumar","year":"2024","journal-title":"Arab. J. Basic Appl. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"100206","DOI":"10.1016\/j.rico.2023.100206","article-title":"Dynamic modelling and optimal control analysis of a fractional order chikungunya disease model with temperature effects","volume":"10","author":"Lusekelo","year":"2023","journal-title":"Results Control Optim."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Gao, D., Lou, Y., He, D., Porco, T.C., Kuang, Y., Chowell, G., and Ruan, S. (2016). Prevention and control of Zika as a mosquito-borne and sexually transmitted disease: A mathematical modeling analysis. Sci. Rep., 6.","DOI":"10.1038\/srep28070"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Rather, I.A., Kumar, S., Bajpai, V.K., Lim, J., and Park, Y.H. (2017). Prevention and control strategies to counter Zika epidemic. Front. Microbiol., 8.","DOI":"10.3389\/fmicb.2017.00305"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","article-title":"Reproduction number and subthreshold endemic equilibria for compartment models of disease transmission","volume":"180","author":"Watmough","year":"2002","journal-title":"Math. Biosci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1007\/s00285-012-0579-9","article-title":"Extending the type reproduction number to infectious disease control targeting contact between types","volume":"67","author":"Shuai","year":"2013","journal-title":"J. Math. Biol."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"LaSalle, J.P. (1976). The Stability of Dynamical Systems, SIAM.","DOI":"10.21236\/ADA031020"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1140\/epjp\/s13360-022-02368-5","article-title":"Mathematical modeling for the transmission potential of Zika virus with optimal control strategies","volume":"137","author":"Ali","year":"2022","journal-title":"Eur. Phys. J. Plus"}],"container-title":["Informatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2227-9709\/11\/4\/85\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:29:52Z","timestamp":1760113792000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2227-9709\/11\/4\/85"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,11]]},"references-count":31,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["informatics11040085"],"URL":"https:\/\/doi.org\/10.3390\/informatics11040085","relation":{},"ISSN":["2227-9709"],"issn-type":[{"type":"electronic","value":"2227-9709"}],"subject":[],"published":{"date-parts":[[2024,11,11]]}}}