{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T14:38:09Z","timestamp":1781620689985,"version":"3.54.5"},"reference-count":62,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2018,10,19]],"date-time":"2018-10-19T00:00:00Z","timestamp":1539907200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2019,6]]},"DOI":"10.1007\/s12190-018-01219-w","type":"journal-article","created":{"date-parts":[[2018,10,19]],"date-time":"2018-10-19T12:03:06Z","timestamp":1539950586000},"page":"387-411","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":53,"title":["Fractional optimal control of an HIV\/AIDS epidemic model with random testing and contact tracing"],"prefix":"10.1007","volume":"60","author":[{"given":"H.","family":"Kheiri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M.","family":"Jafari","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2018,10,19]]},"reference":[{"key":"1219_CR1","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1093\/imammb\/3.4.229","volume":"3","author":"RM Anderson","year":"1986","unstructured":"Anderson, R.M., Medly, G.F., May, R.M., Johnson, A.M.: A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causative agent of AIDS. IMA J. Math. Appl. Med. Biol. 3, 229\u2013263 (1986)","journal-title":"IMA J. Math. Appl. Med. Biol."},{"key":"1219_CR2","doi-asserted-by":"publisher","unstructured":"Egonmwan, A.O., Okuonghae, D.: Analysis of a mathematical model for tuberculosis with diagnosis. J. Appl. Math. Comput. (2018). https:\/\/doi.org\/10.1007\/s12190-018-1172-1","DOI":"10.1007\/s12190-018-1172-1"},{"issue":"1\u20132","key":"1219_CR3","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/s12190-014-0803-4","volume":"48","author":"M Pitchaimani","year":"2015","unstructured":"Pitchaimani, M., Monica, C.: Global stability analysis of HIV-1 infection model with three time delays. J. Appl. Math. Comput. 48(1\u20132), 293\u2013319 (2015). https:\/\/doi.org\/10.1007\/s12190-014-0803-4","journal-title":"J. Appl. Math. Comput."},{"issue":"5","key":"1219_CR4","doi-asserted-by":"publisher","first-page":"1177","DOI":"10.1016\/j.chaos.2004.11.062","volume":"25","author":"L Guihua","year":"2005","unstructured":"Guihua, L., Zhen, J.: Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period. Chaos Soliton Fractals 25(5), 1177\u20131184 (2005)","journal-title":"Chaos Soliton Fractals"},{"key":"1219_CR5","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1016\/j.amc.2006.07.007","volume":"184","author":"A Tripathi","year":"2007","unstructured":"Tripathi, A., Naresh, R., Sharma, D.: Modelling the effect of screening of unaware infectives on the spread of HIV infection. Appl. Math. Comput. 184, 1053\u20131068 (2007)","journal-title":"Appl. Math. Comput."},{"key":"1219_CR6","doi-asserted-by":"publisher","first-page":"333","DOI":"10.3934\/mbe.2009.6.333","volume":"6","author":"Z Mukandavire","year":"2009","unstructured":"Mukandavire, Z., Gumel, A.B., Garira, W., Tchuenche, J.M.: Mathematical analysis of a model for HIV-malaria co-infection. Math. Biosci. Eng. 6, 333\u2013362 (2009)","journal-title":"Math. Biosci. Eng."},{"key":"1219_CR7","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/j.jtbi.2012.11.028","volume":"320","author":"EA Hernandez-Vargasa","year":"2013","unstructured":"Hernandez-Vargasa, E.A., Middleton, R.H.: Modeling the three stages in HIV infection. J. Theor. Biol. 320, 33\u201340 (2013)","journal-title":"J. Theor. Biol."},{"key":"1219_CR8","doi-asserted-by":"publisher","first-page":"1550047","DOI":"10.1142\/S1793524515500473","volume":"08","author":"A Mastroberardino","year":"2015","unstructured":"Mastroberardino, A., Cheng, Y., Abdelrazec, A., Liu, H.: Mathematical modeling of the HIV\/AIDS epidemic in Cuba. Int. J. Biomath. 08, 1550047 (2015). https:\/\/doi.org\/10.1142\/S1793524515500473","journal-title":"Int. J. Biomath."},{"key":"1219_CR9","doi-asserted-by":"publisher","first-page":"1650090","DOI":"10.1142\/S179352451650090X","volume":"09","author":"A Jabbari","year":"2016","unstructured":"Jabbari, A., kheiri, H., Jodayree Akbarfam, A., Bekir, A.: Dynamical analysis of the avian\u2013human influenza epidemic model using multistage analytical method. Int. J. Biomath. 09, 1650090 (2016). https:\/\/doi.org\/10.1142\/S179352451650090X","journal-title":"Int. J. Biomath."},{"key":"1219_CR10","doi-asserted-by":"publisher","first-page":"1650038","DOI":"10.1142\/S1793524516500388","volume":"09","author":"A Mojaver","year":"2016","unstructured":"Mojaver, A., Kheiri, H.: Dynamical analysis of a class of hepatitis C virus infection models with application of optimal control. Int. J. Biomath. 09, 1650038 (2016). https:\/\/doi.org\/10.1142\/S1793524516500388","journal-title":"Int. J. Biomath."},{"key":"1219_CR11","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1016\/j.amc.2005.11.092","volume":"177","author":"J Karrakchou","year":"2006","unstructured":"Karrakchou, J., Rachik, M., Gourari, S.: Optimal control and infectiology: application to an HIV\/AIDS model. Appl. Math. Comput. 177, 807\u2013818 (2006)","journal-title":"Appl. Math. Comput."},{"key":"1219_CR12","doi-asserted-by":"publisher","first-page":"223","DOI":"10.3934\/mbe.2004.1.223","volume":"1","author":"BM Adams","year":"2004","unstructured":"Adams, B.M., Banks, H.T., Kwon Hee-Dae, T.T., Hien, T.: Dynamic multidrug therapies for HIV: optimal and STI control approaches. Math. Biosci. Eng. 1, 223\u2013241 (2004)","journal-title":"Math. Biosci. Eng."},{"issue":"1\u20132","key":"1219_CR13","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1007\/s12190-017-1083-6","volume":"56","author":"A Das","year":"2018","unstructured":"Das, A., Pal, M.: A mathematical study of an imprecise SIR epidemic model with treatment control. J. Appl. Math. Comput. 56(1\u20132), 477\u2013500 (2018). https:\/\/doi.org\/10.1007\/s12190-017-1083-6","journal-title":"J. Appl. Math. Comput."},{"key":"1219_CR14","doi-asserted-by":"publisher","first-page":"2084","DOI":"10.1016\/j.apm.2008.05.017","volume":"33","author":"Z Mukandavire","year":"2009","unstructured":"Mukandavire, Z., Garira, W., Tchuenche, J.M.: Modelling effects of public health educational campaigns on HIV\/AIDS transmission dynamics. Appl. Math. Model. 33, 2084\u20132095 (2009)","journal-title":"Appl. Math. Model."},{"issue":"1\u20132","key":"1219_CR15","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/s12190-012-0597-1","volume":"41","author":"JY Yang","year":"2013","unstructured":"Yang, J.Y., Chen, Y., Zhang, F.Q.: Stability analysis and optimal control of a hand-foot-mouth disease (HFMD) model. J. Appl. Math. Comput. 41(1\u20132), 99\u2013117 (2013). https:\/\/doi.org\/10.1007\/s12190-012-0597-1","journal-title":"J. Appl. Math. Comput."},{"key":"1219_CR16","doi-asserted-by":"publisher","first-page":"3802","DOI":"10.1016\/j.apm.2012.08.004","volume":"37","author":"KO Okosun","year":"2013","unstructured":"Okosun, K.O., Makinde, O.D., Takaidza, I.: Impact of optimal control on the treatment of HIV\/AIDS and screening of unaware infectives. Appl. Math. Model. 37, 3802\u20133820 (2013)","journal-title":"Appl. Math. Model."},{"key":"1219_CR17","first-page":"2701","volume":"8","author":"GG Mwanga","year":"2014","unstructured":"Mwanga, G.G., Aly, S., Haario, H., Nannyonga, B.K.: Optimal control of malaria model with drug resistance in presence of parameter uncertainty. App. Math. Sci. 8, 2701\u20132730 (2014)","journal-title":"App. Math. Sci."},{"key":"1219_CR18","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1016\/j.jtbi.2015.05.022","volume":"380","author":"S Choi","year":"2015","unstructured":"Choi, S., Jung, E., Lee, S.M.: Optimal intervention strategy for prevention tuberculosis using a smoking tuberculosis model. J. Theor. Biol. 380, 256\u2013270 (2015)","journal-title":"J. Theor. Biol."},{"key":"1219_CR19","unstructured":"Okyere, E., Oduro, F.T., Amponsah, S.K., Dontwi, I.K.: Fractional order optimal control model for malaria infection (2016). arXiv preprint arXiv:1607.01612"},{"key":"1219_CR20","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/978-3-642-23068-4_3","volume-title":"Models of Science Dynamics: Encounters Between Complexity Theory and Information Sciences","author":"NK Vitanov","year":"2012","unstructured":"Vitanov, N.K., Ausloos, M.R.: Knowledge epidemics and population dynamics models for describing idea diffusion. In: Scharnhorst, A., Boerner, K., van den Besselaar, P. (eds.) Models of Science Dynamics: Encounters Between Complexity Theory and Information Sciences, pp. 69\u2013125. Springer, Berlin (2012). (Ch. 3)"},{"issue":"2","key":"1219_CR21","doi-asserted-by":"publisher","first-page":"022409","DOI":"10.1103\/PhysRevE.95.022409","volume":"95","author":"M Saeedian","year":"2017","unstructured":"Saeedian, M., Khalighi, M., Azimi Tafreshi, N., Jafari, G.R., Ausloos, M.: Memory effects on epidemic evolution: the susceptible infected recovered epidemic model. Phys. Rev. E 95(2), 022409 (2017)","journal-title":"Phys. Rev. E"},{"issue":"2","key":"1219_CR22","doi-asserted-by":"publisher","first-page":"1","DOI":"10.9734\/BJMCS\/2016\/23017","volume":"14","author":"E Okyere","year":"2016","unstructured":"Okyere, E., Oduro, F.T., Amponsah, S.K., Dontwi, I.K., Frempong, N.K.: Fractional order SIR model with constant population. Br. J. Math. Comput. Sci. 14(2), 1\u201312 (2016)","journal-title":"Br. J. Math. Comput. Sci."},{"issue":"1","key":"1219_CR23","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1140\/epjst\/e2011-01390-6","volume":"193","author":"HG Sun","year":"2011","unstructured":"Sun, H.G., Chen, W., Wei, H., chen, Y.Q.: A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems. Eur. Phys. J. Spec. Top. 193(1), 185\u2013192 (2011)","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"1219_CR24","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-18101-6","volume-title":"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation","author":"I Petras","year":"2011","unstructured":"Petras, I.: Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation. Springer, Berlin (2011)"},{"key":"1219_CR25","volume-title":"Fractional Differential Equations, Mathematics in Science and Engineering","author":"I Podlubny","year":"1999","unstructured":"Podlubny, I.: Fractional Differential Equations, Mathematics in Science and Engineering. Academic Press, San Diego (1999)"},{"key":"1219_CR26","doi-asserted-by":"crossref","unstructured":"Rihan, F.A.: Numerical modeling of fractional-order biological systems. Abstr. Appl. Anal. 2013, Article ID 816803 (2013)","DOI":"10.1155\/2013\/816803"},{"issue":"3","key":"1219_CR27","doi-asserted-by":"publisher","first-page":"525","DOI":"10.1016\/j.sigpro.2010.01.027","volume":"91","author":"HG Sun","year":"2011","unstructured":"Sun, H.G., chen, Y.Q., Chen, W.: Random-order fractional differential equation models. Signal Process. 91(3), 525\u2013530 (2011)","journal-title":"Signal Process."},{"key":"1219_CR28","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1016\/j.chaos.2017.03.066","volume":"102","author":"W Chen","year":"2017","unstructured":"Chen, W., Liang, Y.: New methodologies in fractional and fractal derivatives modeling. Chaos Solitons Fractals 102, 72\u201377 (2017)","journal-title":"Chaos Solitons Fractals"},{"key":"1219_CR29","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.amc.2014.05.061","volume":"242","author":"CMA Pinto","year":"2014","unstructured":"Pinto, C.M.A., Carvalho, A.R.M.: New findings on the dynamics of hiv and tb coinfection modelsl. Appl. Math. Comput. 242, 36\u201346 (2014)","journal-title":"Appl. Math. Comput."},{"key":"1219_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1753-4631-4-1","volume":"4","author":"E Ahmed","year":"2010","unstructured":"Ahmed, E., El-Saka, H.A.: On fractional order models for hepatitis C. Nonlinear Biomed. Phys. 4, 1\u20133 (2010)","journal-title":"Nonlinear Biomed. Phys."},{"key":"1219_CR31","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1016\/j.mcm.2009.04.019","volume":"50","author":"Y Ding","year":"2009","unstructured":"Ding, Y., Ye, H.: A fractional-order differential equation model of HIV infection of CD4+ T-cells. Math. Comput. Model. 50, 386\u2013392 (2009)","journal-title":"Math. Comput. Model."},{"key":"1219_CR32","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1016\/j.cam.2018.06.055","volume":"346","author":"H Kheiri","year":"2018","unstructured":"Kheiri, H., Jafari, M.: Stability analysis of a fractional order model for the HIV\/AIDS epidemic in a patchy environment. J. Comput. Appl. Math. 346, 323\u2013339 (2018)","journal-title":"J. Comput. Appl. Math."},{"key":"1219_CR33","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1016\/j.amc.2017.08.048","volume":"316","author":"J Singh","year":"2018","unstructured":"Singh, J., Kumar, D., Hammouch, Z., Atangana, A.: A fractional epidemiological model for computer viruses pertaining to a new fractional derivative. Appl. Math. Comput. 316, 504\u2013515 (2018)","journal-title":"Appl. Math. Comput."},{"key":"1219_CR34","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.amc.2018.04.025","volume":"335","author":"J Singh","year":"2018","unstructured":"Singh, J., Kumar, D., Baleanu, D., Rathore, S.: An efficient numerical algorithm for the fractional Drinfeld\u2013Sokolov\u2013Wilson equation. Appl. Math. Comput. 335, 12\u201324 (2018)","journal-title":"Appl. Math. Comput."},{"key":"1219_CR35","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1140\/epjp\/i2018-11934-y","volume":"133","author":"J Singh","year":"2018","unstructured":"Singh, J., Kumar, D., Baleanu, D.: A new analysis of Fornberg-Whitham equation pertaining to a fractional derivative with Mittag\u2013Leffler type kernel. Eur. Phys. J. Plus 133, 70 (2018). https:\/\/doi.org\/10.1140\/epjp\/i2018-11934-y","journal-title":"Eur. Phys. J. Plus"},{"key":"1219_CR36","doi-asserted-by":"publisher","first-page":"103113","DOI":"10.1063\/1.4995032","volume":"27","author":"J Singh","year":"2017","unstructured":"Singh, J., Kumar, D., Baleanu, D.: On the analysis of chemical kinetics system pertaining to a fractional derivative with Mittag\u2013Leffler-type kernel. Chaos 27, 103113 (2017)","journal-title":"Chaos"},{"key":"1219_CR37","doi-asserted-by":"publisher","first-page":"408","DOI":"10.1016\/j.physa.2018.02.045","volume":"501","author":"s He","year":"2018","unstructured":"He, s, Banerjee, S.: Epidemic outbreaks and its control using a fractional order model with seasonality and stochastic infection. Physica A 501, 408\u2013417 (2018)","journal-title":"Physica A"},{"key":"1219_CR38","doi-asserted-by":"publisher","unstructured":"Hsieh, Y.H., de Arazoza, H., Lounes, R., Joanes, J.: A class of methods for HIV contact tracing in Cuba: implications for intervention and treatment. Determ. Stoch. Models AIDS Epidemics HIV Infect. Interv. (2005). https:\/\/doi.org\/10.1142\/9789812569264-0004","DOI":"10.1142\/9789812569264-0004"},{"key":"1219_CR39","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/s11071-004-3764-6","volume":"38","author":"OP Agrawal","year":"2004","unstructured":"Agrawal, O.P.: A general formulation and solution scheme for fractional optimal control problems. Nonlinear Dyn. 38, 323\u2013337 (2004)","journal-title":"Nonlinear Dyn."},{"key":"1219_CR40","doi-asserted-by":"publisher","first-page":"011010-1","DOI":"10.1115\/1.2814055","volume":"130","author":"OP Agrawal","year":"2008","unstructured":"Agrawal, O.P.: A quadratic numerical scheme for fractional optimal control problems. J. Dyn. Syst. Meas. Control 130, 011010-1\u2013011010-6 (2008)","journal-title":"J. Dyn. Syst. Meas. Control"},{"key":"1219_CR41","first-page":"1","volume":"44","author":"FA Basir","year":"2015","unstructured":"Basir, F.A., Elaiw, A.M., Kesh, D., Roy, P.K.: Optimal control of a fractional-order enzyme kinetic model. Control Cybern. 44, 1\u201318 (2015)","journal-title":"Control Cybern."},{"key":"1219_CR42","doi-asserted-by":"publisher","unstructured":"Sweilam, N.H., Al-Mekhla, S.M.: On the optimal control for fractional multi-strain TB model. Optim. Control Appl. Methods (2016). https:\/\/doi.org\/10.1002\/oca.2247","DOI":"10.1002\/oca.2247"},{"key":"1219_CR43","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1109\/TCST.2011.2153203","volume":"13","author":"Y Ding","year":"2012","unstructured":"Ding, Y., Wang, Z., Ye, H.: Optimal control of a fractional-order HIV-immune system with memory. IEEE Trans. Control Syst. Technol. 13, 763\u2013769 (2012)","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"1219_CR44","doi-asserted-by":"crossref","DOI":"10.1201\/9781420011418","volume-title":"Optimal Control Applied to Biological Models","author":"S Lenhart","year":"2007","unstructured":"Lenhart, S., Workman, T.: Optimal Control Applied to Biological Models. Chapman and Hall, New York (2007)"},{"key":"1219_CR45","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/s10589-011-9454-7","volume":"53","author":"M McAsey","year":"2012","unstructured":"McAsey, M., Mou, L., Han, H.: Convergence of the forward\u2013backward sweep method in optimal control. Comput. Optim. Appl. 53, 207\u2013226 (2012)","journal-title":"Comput. Optim. Appl."},{"key":"1219_CR46","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1023\/A:1016592219341","volume":"29","author":"K Diethelm","year":"2002","unstructured":"Diethelm, K., Ford, N.J., Freed, A.D.: A predictor\u2013corrector approach for the numerical solution differential equations. Nonlinear Dyn. 29, 3\u201322 (2002)","journal-title":"Nonlinear Dyn."},{"key":"1219_CR47","first-page":"31","volume":"35","author":"K Diethelm","year":"2004","unstructured":"Diethelm, K., Ford, N.J., Freed, A.D.: Detailed error analysis for a fractional Adams method. Nonlinear Dyn. 35, 31\u201352 (2004)","journal-title":"Nonlinear Dyn."},{"key":"1219_CR48","volume-title":"Theory and Application of Fractional Differential Equations","author":"AA Kilbas","year":"2006","unstructured":"Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Application of Fractional Differential Equations. Elsevier, New York (2006)"},{"key":"1219_CR49","volume-title":"Fractional Integrals and Derivatives-Theory and Applications","author":"SG Samko","year":"1993","unstructured":"Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives-Theory and Applications. Gordon and Breach, Linghorne (1993)"},{"key":"1219_CR50","volume-title":"The Analysis of Fractional Differential Equations, An Application-Oriented Exposition Using Operators of Caputo Type","author":"K Diethelm","year":"2004","unstructured":"Diethelm, K.: The Analysis of Fractional Differential Equations, An Application-Oriented Exposition Using Operators of Caputo Type. Springer, Berlin (2004)"},{"key":"1219_CR51","volume-title":"Cuba\u2019s HIV\/AIDS Strategy: An Integrated, Rights-Based Approach","author":"C Gorry","year":"2008","unstructured":"Gorry, C.: Cuba\u2019s HIV\/AIDS Strategy: An Integrated, Rights-Based Approach. Oxfam International, Havana (2008)"},{"key":"1219_CR52","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1016\/j.amc.2006.07.102","volume":"186","author":"ZM Odibat","year":"2007","unstructured":"Odibat, Z.M., Shawagfeh, N.T.: Generalized Taylors formula. Appl. Math. Comput. 186, 286\u2013293 (2007)","journal-title":"Appl. Math. Comput."},{"key":"1219_CR53","doi-asserted-by":"publisher","first-page":"709","DOI":"10.1016\/j.jmaa.2006.10.040","volume":"332","author":"W Lin","year":"2007","unstructured":"Lin, W.: Global existence theory and chaos control of fractional differential equations. J. Math. Anal. Appl. 332, 709\u2013726 (2007)","journal-title":"J. Math. Anal. Appl."},{"key":"1219_CR54","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","volume":"180","author":"P Driessche van den","year":"2002","unstructured":"van den Driessche, P., Watmough, J.: Reproduction numbers and sub-threshhold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180, 29\u201348 (2002)","journal-title":"Math. Biosci."},{"key":"1219_CR55","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1007\/s11071-012-0601-1","volume":"71","author":"C Li","year":"2013","unstructured":"Li, C., Ma, Y.: Fractional dynamical systemand its linearization theorem. Nonlinear Dyn. 71, 621\u2013633 (2013)","journal-title":"Nonlinear Dyn."},{"key":"1219_CR56","volume-title":"Higher Algebra","author":"AM Mishina","year":"1965","unstructured":"Mishina, A.M., Proskuryako, I.V.: Higher Algebra. Nauka, Moscow (1965)"},{"key":"1219_CR57","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1016\/j.nonrwa.2015.05.014","volume":"26","author":"J Huo","year":"2015","unstructured":"Huo, J., Zhao, H., Zhu, L.: The effect of vaccines on backward bifurcation in a fractional order HIV model. Nonlinear Anal. RWA 26, 289\u2013305 (2015)","journal-title":"Nonlinear Anal. RWA"},{"issue":"9","key":"1219_CR58","doi-asserted-by":"publisher","first-page":"2951","DOI":"10.1016\/j.cnsns.2014.01.022","volume":"19","author":"N Aguila-Camacho","year":"2014","unstructured":"Aguila-Camacho, N., Duarte-Mermoud, M.A., Gallegos, J.A.: Lyapunov functions for fractional order systems. Commun. Nonlinear Sci. Numer. Simul. 19(9), 2951\u20132957 (2014)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"1219_CR59","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1080\/00207178908953385","volume":"50","author":"OP Agrawal","year":"1989","unstructured":"Agrawal, O.P.: General formulation for the numerical solution of optimal control problems. Int. J. Control 50, 627\u2013638 (1989)","journal-title":"Int. J. Control"},{"issue":"2","key":"1219_CR60","first-page":"49","volume":"5","author":"AE Meiberg","year":"2008","unstructured":"Meiberg, A.E., Bos, A.E.R., Onya, H.E., Schaalma, H.P.: Fear of stigmatization as barrier to voluntary HIV counselling and testing in South Africa. East Afr. J. Public Health 5(2), 49\u201354 (2008)","journal-title":"East Afr. J. Public Health"},{"key":"1219_CR61","doi-asserted-by":"publisher","first-page":"545","DOI":"10.3934\/mbe.2006.3.545","volume":"3","author":"B Rapatski","year":"2006","unstructured":"Rapatski, B., Klepac, P., Duecks, S., Liu, M., Weiss, L.I.: Mathematical epidemiology of HIV\/AIDS in Cuba during the period 1986\u20132000. Math. Biosci. Eng. 3, 545\u2013556 (2006)","journal-title":"Math. Biosci. Eng."},{"key":"1219_CR62","volume-title":"Mathematical Modeling of the HIV\/AIDS Epidemic in Cuba","author":"T Mastroberardino","year":"2014","unstructured":"Mastroberardino, T.: Mathematical Modeling of the HIV\/AIDS Epidemic in Cuba. AMS Eastern Sectional Meeting University of Maryland, Baltimore County (2014)"}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-018-01219-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12190-018-01219-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-018-01219-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,4]],"date-time":"2022-09-04T08:24:19Z","timestamp":1662279859000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12190-018-01219-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,19]]},"references-count":62,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["1219"],"URL":"https:\/\/doi.org\/10.1007\/s12190-018-01219-w","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,19]]},"assertion":[{"value":"3 June 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 October 2018","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}