CINXE.COM

Just a moment...

<!DOCTYPE html><html lang="en-US"><head><title>Just a moment...</title><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="robots" content="noindex,nofollow"><meta name="viewport" content="width=device-width,initial-scale=1"><style>*{box-sizing:border-box;margin:0;padding:0}html{line-height:1.15;-webkit-text-size-adjust:100%;color:#313131;font-family:system-ui,-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji}body{display:flex;flex-direction:column;height:100vh;min-height:100vh}.main-content{margin:8rem auto;max-width:60rem;padding-left:1.5rem}@media (width <= 720px){.main-content{margin-top:4rem}}.h2{font-size:1.5rem;font-weight:500;line-height:2.25rem}@media (width <= 720px){.h2{font-size:1.25rem;line-height:1.5rem}}#challenge-error-text{background-image:url(data:image/svg+xml;base64,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);background-repeat:no-repeat;background-size:contain;padding-left:34px}@media (prefers-color-scheme:dark){body{background-color:#222;color:#d9d9d9}}</style><meta http-equiv="refresh" content="120"></head><body class="no-js"><div class="main-wrapper" role="main"><div class="main-content"><noscript><div class="h2"><span id="challenge-error-text">Enable JavaScript and cookies to continue</span></div></noscript></div></div><script>(function(){window._cf_chl_opt={cvId: '3',cZone: "publications.waset.org",cType: 'non-interactive',cRay: '913587d349605f57',cH: 'pNMBJMp02XO5FUO0vIJEPXX4Y7CNiMfDqs4aqrGVkgA-1739792719-1.2.1.1-FtmboVFAijbCpwMciwmP_VgoW9ItbRSo.bg_TSWOcO4iJW8Zr5xg10Bu4oype_RQ',cUPMDTk: "\/abstracts\/search?q=mathematical%20models&__cf_chl_tk=Vufutq.uS7TZGLLZuWWA2Ke2L4jm5C9WvexXuzc3AzI-1739792719-1.0.1.1-GWYBjArug.0l.r5XxtSF6g98hQI7XcT_rE_G2hz6Hyg",cFPWv: 'b',cITimeS: '1739792719',cTTimeMs: '1000',cMTimeMs: '120000',cTplC: 0,cTplV: 5,cTplB: 'cf',cK: "",fa: "\/abstracts\/search?q=mathematical%20models&__cf_chl_f_tk=Vufutq.uS7TZGLLZuWWA2Ke2L4jm5C9WvexXuzc3AzI-1739792719-1.0.1.1-GWYBjArug.0l.r5XxtSF6g98hQI7XcT_rE_G2hz6Hyg",md: "zRajLi_Sb.USpM9hnI9qs2tacBCV8Bej3bP5c1tnXE8-1739792719-1.2.1.1-K0twVmfwn4TF0q6aP8JX2yqThfUL_YFy3Zh9druR4RfO7WeYC.zPKuw9lQlpG4aFZvzgoKjV5VbSmOOnoinTyBhw2FA2c2jQDDMQP.RjvEIHPkd5bFOQYmhg5_suBxpJu._hWcouX5pOZBNZZnOA8jkCZL66_1wdwyF4jko6l.CNtElTHP5snxUqSSknaY_VEsHDiaHe1ejpOfrgeG3Ufg4JC6S3zKB7jSkh8lj4YZV.UiTYuyUx20wYxQoCp.kNtzrjFax9FlwkH6NlkiyZIpnDzIfYySkGgIXPijmC48ClvQi_pTYg_5ONu1Aq6bXN5.11wVp5qZHd1z4CKwMVyV6lib9hLRjzGengpIv3kGDzUQbGlfAWe5KFZxS_BGK7gpo4IGRNZovYcbdwXkX2vxA4t1ZbtXRFQqghLANBWMpS7r0WWfqqBj41tmtbRZvBMNYF9sFkBWg5_8RoqYNxScIqqqIQ7.5.6c6feUan67h3IjdEfi5GjxRkP8SaVKE6Att576ee43oUFrX5Xpy3L2lzQfRsmf9S7fWZRUU8.G.6uIjkKs8ynOSXu.Z5nO0AjAb10PC8wdP52mawXM16f9RIA4R4zITbTx5mzIeOa.ndGWbnwk.dinZORVKnNn88clUU9pIJTU.NYYcLLSGh.x7ztdf9hrZWJc28M4s7_r8QlWYk9844dHGGbBJMtEljBil24V82L.dTIXCGgCFFHeNoqsjgSim63WUpC0fLFgq59Ffb.tD7Cwg6gJVdTxeDN_DxAaoTzb.9W_gp6uTIXdt.wiSkl_X8Mk9d9.LMl46qLnd7hwlksR27.UPngiTRaEx6Yx7MX8lJToLvUwN3lsnDElV4e2Wi871QDhWiVQ.FMPsfm9J0bHnD3TTEt3DD7o_nq0jlxp6OZqhIjX7.2YLCp_MNfnGylE8iUXSoYOD7O04A_4lpdD_cjt.AHbNHTG3SndOQWpPmWr9c4xHrC8Ni2fHnNAgCRHQ162lS3xIQ7rU69MaGF11erPOL0EKOXlZsixeDXmuDAyd64E3hpUqoFvyeSqMOm_.H4egiGxQwOhlTtT_GoFHe52dwsMwwyafzEIHUco.txWccQoUoPffSx9bUhQHB3mFMkzlrIGie.jqGNSKKTaMk_C1VkJ2UH9Xs6Bp1SUEjTzIjhQK9kbO43.cH_cNx49UlJkrNe57euLRlXdKZQr4Os0cYMKh27l79eI4UmXpTNFX7NA8EKPzSfYE0SlZK3O4Ed2pw6Dtb2G1kLFx75QGJ9Z3yUkZ2URPS4RLj_IoNR7VJEiv9A2vX_di6YN.DcvYrcKdqFmlR1hM6EoK65Sn82mL2vRmNzLPEQ9OGqp2VE3Uh8HfC7W6ZF.6iik1JuKqzuQp88gecju5ACQqqAOE1IsrTzaVszftDUUgen08lVInenb.mnyPTnyGpWmcSoMYBIafpWV2RrPaeynnvsLIUcNHd50rUB15xwb8fwNrseJHcKhQGu9foNoddmz1VaI3bEbdQRclJmCegvMVZ.EAJ7OLSAJAKPpwxDTYTJ7BCYlXV_EjsCJ9ViXXlbfIKMOpgxP3cZioLkkFZjVi1EEnUnRc_9SyOVQuZrjoDPZR3dPzQILreBLiIABo3_uDElhSkuqxuJePx0dMe52RwE1mUqDnzbrSx0WKnr8Q92qxK7Jts4anllU0tK2vDrDBcNqX3VqYMqIO_fxTE4WzsVrTzN_RpMlQlDGVvAQDzqKUPlwkvBDX8rbpT6DLr.aO3l1P3maGtEeaQh0P6ZlQo.PsTbbLKRSBel6HMQcc1pFtiiAVAMkLIRlAbbDX3G4.XyN_L_D8rmOjyo.AwdiCzpO0uFskElk.qobnVMF6ebPNWkQJ2yiQa2CxbWUXCUe7kn6J4keXh4FvKSv0tpf19rIS36FJds1M8g9l2RX3tzEy3WZTcgWy.vrO39_Gp4KAoGbcHcu2ct01A_2Wj6Ds01tTJxrKhW8tE",mdrd: ".7.c1u0igyLaPnQPv6n0fah_iX27KnkvXXg0KMjrw70-1739792719-1.2.1.1-muIRDlwsJKTqmDVAGj_jfVvYfwFQVku08VJmyKp9rkE2RaySvILZ5jSYW9QRGbLepOpPXNy1ZzjAynaBDvgf.WUMyMRgb9NNN_IP6Rv.epqHmOMTqrpsEPevPrlrMqq.9Hx1Av5UyF6ueJJL7loFvOb5uk_2bACQdvaR84OCtkzc64VVJhmwtAN4rEOn03SW_Xc8EecnWS.EhL5MuHrGfEtALtdAYH4kIKuLqGDJp28.ety7C29UCMUgMUFOH4dmZneAVCa8AvZk7Dvnar6o0atMWWWs4r7ti.ZryccDa6YLq8LiQGRC4Wqz1d9dtX7IYxpzxqzd5TW.OkB5AYKHcE1XKBaffHsSN5onvqcCmYHDTVKHlPZjVQ44gsSn6xdc8uochlKjkE6sd57Zljo9hVxlHi0FvPPknmfh8xxyiM.DjSXPeOPidhOrD6W1mz4x.rr3nmCaTUnEqpzyl56XNR9ioSOsQ4t1FKhKIccJX1N6n4HSr0bB9utZwjQvw_ALVq7aoI2FSgACL_lAPYK51ob4VdzGsShDysNZMg_Ba9LldYwVyelDw_o5osHpE.Lj6BxLdSUYRtZm1u5alIS9VM3poH87XzH60mlyVUtXrMI1qcNfzkuYSIQDQ7sp7S8UuK8_xAQ_RBcGH3MUqGzgqJ6h3OsxfYNNGpnQ_Dt5L02Wb2MU4rZdoOWVLklhpADVgLSTRrK9cXW01QI9viXhub5HkRQlLsf3MZosKAhbJOWVYCuMWgRxK4K4WUDd7FgLKZnE5eAvkDscTeCrhF7zYcrM_hkUiR3vyVDx7r.60GJPcGfFE3KS_owdo74DVgV2WeEwEQ7Ga4oEoR3saAOWSSNFk.R.cPXOwiWN3nJt3a2D0wsWPQj7f9wsVUWCnOJbNzAA2fh78ccqD0vDYjDjIUYJ3nhog1mXl3NaSsJo208Gk7Cbgol9xcqbDcUaVwiIHTKoVG5HzIW28v7yaO33ejgdzg9kQ8ZwcZ5SWK7fJGGquPlfM2If98OVWK.kDySOtJ_peA1Iv1XbW7Z1dZ0DTYOag2gRWLTGP1T_zOzfWnC_rg46DVNU2DwPTleb8axj7Rc9wRHQpN0A7idSrn4mSoHqZf7_qD7pIjlbW9r1EvQZuVT2M8ABUE5r8NsjyNVoleZYXtWTcucVT3eZe3GmG8BUh_LTSA7oWwo3JpCxyBgiNUbZTsA3FTzpb777e_cGjqUmHCSEXx9jbxuilmcyB9zGYPqp6BYLOgvSAC30IZyO.a.D4a8dDPqUyRTxxlGRVCdIL0wisiI5jBV3KiJD2zm9t1KMhZxflVGJP.wVODXBMK2V2_4ZSPfwV3VYXMsxhvP8Z3FbYE7baRio10GAG9oP8jmbd6etnHUvdke9xkNl8Xxri3YrTlDaWnAIc9EVOB.pyzmFd9GJaHh0Rv4w2.MbpK5BHQR9djLPvA9v22h5HCI30KM7MLbFOyh2TovTPzVR0_glnOXOq7SFyQgvNs_H010_nOJy8YzrgDAUcH.voM3LoQbTRjsHiEF5UHDeF4dyFvSPcEJC0Pyaw_KV135XwoLCBIkxU5LtzrJGmxUegzxlx20H5VGM4rt_TSOaki9h0RDYHpJOAZdcsZKhXLt2JdN_FhWqZwWuw37vx7HDGYNd1izF41IOOTf3Ln95QkGfwCN3HjR.n4wk.2mkCn.iQe3aIF.GiYLDk2Z4W5ioAZHLCqAmZLqhmEvDvkDUNFHb5ncbhAYDjEZLcoE2Os2Risb7AD12ERdA4t5R58gy1jV1uVYtukbmYbLEbtSKwPO6e_aDiZ1m0tHly3cWODWuLOFJviQVtB98y8pEUbza7yZA6ADjVFMTqHCxdT0eqM.YVq3nGu9nbXruy6qOo_0eIdsnVotGiDaLubIGCMMTWxIHOFnH5HLdYfGQLfZ6rknlpd6lwPFlxHadSUvCzyCjfVAFpRxok8u.EDC7zfYd9rkFFSpcgEqrp28MojaK0Tp.yaaMgqV.RNcTl7ufhg"};var cpo = document.createElement('script');cpo.src = '/cdn-cgi/challenge-platform/h/b/orchestrate/chl_page/v1?ray=913587d349605f57';window._cf_chl_opt.cOgUHash = location.hash === '' && location.href.indexOf('#') !== -1 ? '#' : location.hash;window._cf_chl_opt.cOgUQuery = location.search === '' && location.href.slice(0, location.href.length - window._cf_chl_opt.cOgUHash.length).indexOf('?') !== -1 ? '?' : location.search;if (window.history && window.history.replaceState) {var ogU = location.pathname + window._cf_chl_opt.cOgUQuery + window._cf_chl_opt.cOgUHash;history.replaceState(null, null, "\/abstracts\/search?q=mathematical%20models&__cf_chl_rt_tk=Vufutq.uS7TZGLLZuWWA2Ke2L4jm5C9WvexXuzc3AzI-1739792719-1.0.1.1-GWYBjArug.0l.r5XxtSF6g98hQI7XcT_rE_G2hz6Hyg" + window._cf_chl_opt.cOgUHash);cpo.onload = function() {history.replaceState(null, null, ogU);}}document.getElementsByTagName('head')[0].appendChild(cpo);}());</script></body></html>