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Globa. properties of nonlinea. hum.ra. im.unity vira. infection m.dels

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Interna.iona. Journa. of Biom.0}hem.0}ics 2015年第5期8卷 53-105页

作者： a. m. elaiw H. a.Sha.ra.i' Depa.tm.nt of m.0}hem.0}ics Faculty of Science King Abdulaziz University P. O. Box 80203 Jeddah 21589 Saudi Arabia Depa.tm.nt of m.0}hem.0}ics Faculty of Science AI-Azhar University Assiut 71511 Egypt

In this pa.er, we consider two nonlinea. m.dels for vira. infection with hum.ra. im.u- nity. The first m.del conta.ns four com.a.tm.nts; uninfected ta.get cells, a.tively infected cells, free virus pa.ticles a.d B cells. The second m.del is a.m.difica.ion of the first one by including the la.ently infected cells. The incidence ra.e, rem.va. ra.e of infected cells, production ra.e of viruses a.d the la.ent-to-a.tive conversion ra.e a.e given by m.re genera. nonlinea. functions. We ha.e esta.lished a.set of conditions on these genera. functions a.d determ.ned two threshold pa.a.eters for ea.h m.del which a.e sufficient to determ.ne the globa. dyna.ics of the m.dels. The globa. a.ym.totic sta.ility of a.l equilibria.of the m.dels ha. been proven by using Lya.unov theory a.d a.plying La.a.le＇s inva.ia.ce principle. We ha.e perform.d som. num.rica. sim.la.ions for the m.dels with specific form. of the genera. functions. We ha.e shown tha., the num.rica. results a.e consistent with the theoretica. results.

关键词： Vira. infection globa. sta.ility hum.ra. im.une response Lya.unov func-tion.

Globa. properties of a.cell m.dia.ed im.unity in HIV infection m.del with two cla.ses of ta.get cells a.d distributed dela.s

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Interna.iona. Journa. of Biom.0}hem.0}ics 2014年第5期7卷 119-143页

作者： a. m. elaiw R. m. a.ukwa.k E. O. a.za.ra.i Depa.tm.nt of m.0}hem.0}ics Faculty of Science King Abdulaziz University P. O. Box 80203 Jeddah 21589 Saudi Arabia Depa.tm.nt of m.0}hem.0}ics Faculty of Science AI-Azhar University Assiut Egypt

In this pa.er, we study the globa. properties of a.hum.0} im.unodeficiency virus （HIV） infection m.del with cytotoxic T lym.hocytes （CTL） im.une response. The m.del is a.six-dim.nsiona. tha. describes the intera.tion of the HIV with two cla.ses of ta.get cells, CD4＋ T cells a.d m.0}ropha.es. The infection ra.e is given by sa.ura.ion functiona. response. Two types of distributed tim. dela.s a.e incorpora.ed into the m.del to describe the tim. needed for infection of ta.get cell a.d virus replica.ion. Using the m.thod of Lya.unov functiona., we ha.e esta.lished tha. the globa. sta.ility of the m.del is determ.ned by two threshold num.ers, the ba.ic infection reproduction num.er R0 a.d the im.une response a.tiva.ion num.er R0. We ha.e proven tha. if R0 ≤ 1, then the uninfected stea.y sta.e is globa.ly a.ym.totica.ly sta.le （Ga.）, if R0≤ 1 〈 R0, then the infected stea.y sta.e without CTL im.une response is Ga., a.d if R0〉 1, then the infected stea.y sta.e with CTL im.une response is Ga..

关键词： Globa. sta.ility HIV dyna.ics dela. cell m.dia.ed im.unity.

a.a.ysis of within-host CHIKV dyna.ics m.dels with genera. incidence ra.e

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Interna.iona. Journa. of Biom.0}hem.0}ics 2018年第5期11卷 17-41页

作者： a.m.d m. elaiw Ta.feek O. a.a.e Sa.d m. a.sula.i Depa.tm.nt of m.0}hem.0}ics Faculty of Science King Abdulaziz University P.O. Box 80203 Jeddah 21589 Saudi Arabia

In this pa.er we study the sta.ility a.a.ysis of two within-host Chikungunya.virus （CHIKV） dyna.ics m.dels. The incidence ra.e between the CHIKV a.d the uninfected m.uocytes is m.deled by a.genera. nonlinea. function. The second m.del considers two types of infected m.nocytes （i） la.ently infected m.nocytes which do not genera.e CHIKV a.d （ii） a.tively infected m.nocytes which produce the CHIKV pa.ticles. Sufficient conditions a.e found which gua.a.tee the globa. sta.ility of the positive stea.y sta.es. Using the Lya.unov function, we esta.lished the globa. sta.ility of the stea.y sta.es of the m.dels. The theoretica. results a.e confirm.d by num.rica. sim.la.ions.

关键词： Globa. sta.ility chikungunya.virus infection genera. incidence ra.e Lya.unov function.

Im.a.t of a.a.tive im.une response a.d cellula. infection on dela.ed virus dyna.ics with m.lti-sta.es of infected cells

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Interna.iona. Journa. of Biom.0}hem.0}ics 2020年第1期13卷 79-140页

作者： a.m.elaiw N.H.a.Sha.ra.i Depa.tm.nt of m.0}hem.0}ics Faculty of Science King Abdulaziz UniversityP.O.Box 80203 Jeddah 21589Saudi Arabia Depa.tm.nt of m.0}hem.0}ics Faculty of Science University of JeddahP.O.Box 80327 Jeddah 21589Saudi Arabia

In this investiga.ion,we propose a.d a.a.yze a.virus dyna.ics m.del with m.lti-sta.es of infected *** m.del incorpora.es the effect of both hum.ra. a.d cell-m.dia.ed im.une *** consider two m.des of tra.sm.ssions,virus-to-cell a.d *** intra.ellula. discrete-tim. dela.s ha.e been integra.ed into the *** incidence ra.e of infection a. well a. the genera.ion a.d rem.va. ra.es of a.l com.a.tm.nts a.e described by genera. nonlinea. *** derive five threshold pa.a.eters which determ.ne the existence of the equilibria.of the m.del under considera.ion.a.set of conditions on the genera. functions ha. been esta.lished which is sufficient to investiga.e the globa. sta.ility of the five equilibria.of the *** globa. a.ym.totic sta.ility of a.l equilibria.is proven by utilizing Lya.unov function a.d La.a.le’s inva.ia.ce *** theoretica. results a.e illustra.ed by num.rica. sim.la.ions of the m.del with specific form. of the genera. functions.

关键词： Vira. a.d cellula. infections globa. sta.ility a.a.tive im.une response Lya.unov function m.lti-sta.ed infected cells.

Globa. a.a.ysis of a.rea.tion-diffusion blood-sta.e m.0}a.ia.m.del with im.une response

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Interna.iona. Journa. of Biom.0}hem.0}ics 2020年第4期13卷 201-231页

作者： a.m.elaiw a.D.a. a.ha Depa.tm.nt of m.0}hem.0}ics Fa.ulty of Science King Abdulaziz University P.O.Box 80203Jeddah 21589Saudi Arabia

m.0}a.ia.is one of the m.st da.gerous disea.es tha. threa.ens people's lives a.ound the *** this pa.er,we study a.rea.tion-difusion m.del for the within-host dyna.ics of m.0}a.ia.infection with a. a.tibody im.une *** m.del is given by a.system.of pa.tia. differentia. equa.ions(PDEs)to describe the blood-sta.e of m.0}a.ia.life *** a.dresses the intera.tions between uninfected red blood cells,a.tibodies,a.d three types of infected red blood cells,na.ely ringinfected red blood cells,trophozoite-infected red blood cells a.d schizont-infected red blood ***,the m.del conta.ns a.pa.a.eter to m.a.ure the effica.y of isoleucinc sta.va.ion a.d its effect on the growth of m.0}a.ia.*** show the ba.ic properties of the *** com.ute a.l equilibria.a.d derive the thresholds from.the conditions of existence of m.0}a.ia.equilibrium.*** prove the globa. sta.ility of a.l equilibrium.points ba.ed on choosing suita.le Lya.unov *** use the cha.a.teristic equa.ions to verify the loca. insta.ility of equilibrium.*** fina.ly execute num.rica. sim.la.ions to va.ida.e the theoretica. results a.d highlight som. im.orta.t *** results indica.e tha. isoleucine sta.va.ion ca. ha.e a.critica. im.a.t on the sta.ility of equilibrium.*** the effica.y of isoleucine sta.va.ion is high,it switchcs the system.from.the infection sta.e to the m.0}a.ia.free *** presence of a. a.tibody im.une response does not lea. to the elim.na.ion of m.0}a.ia.infection,but it suppresses the growth of m.0}a.ia.pa.a.ites a.d increa.es the a.ount of hea.thy red blood cells.

关键词： Pla.m.dium.fa.cipa.um diffusion globa. sta.ility isoleucine sta.va.ion a.ti-body irnm.nity

m.deling a.d sta.ility a.a.ysis of HIV/HTLV-I co-infection

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Interna.iona. Journa. of Biom.0}hem.0}ics 2021年第5期14卷 97-143页

作者： a.m.elaiw N.H.a.Sha.ra.i Depa.tm.nt of m.0}hem.0}ics Fa.ulty of Science King Abdulaziz University P.O.Box 80203Jeddah 21589Saudi Arabia Depa.tm.nt of m.0}hem.0}ics Faculty of Science Al-Azhar UniversityAssiut BranchAssiutEgypt Depa.tm.nt of m.0}hem.0}ics Fa.ulty of Science University of Jeddah P.O.Box 80327Jeddah 21589Saudi Arabia

Hum.0} im.unodeficiency virus(HIV)a.d hum.0} T-Iym.hotropic virus type I(HTLV-I)a.e two retroviruses tha. infect the susceptible CD4^(+)T *** is known tha. HIV a.d HTLV-I ha.e in com.on a.wa. of tra.sm.ssion through direct conta.t with certa.n body fluids rela.ed to infected ***,it is not surprising tha. a.m.no-infected person with one of these viruses ca. be co-infected with the other *** the litera.ure,a.grea. num.er of m.0}hem.0}ica. m.dels ha. been presented to describe the within-host dyna.ics of HIV or HTLV-I ***,the within-host dyna.ics of HIV/HTLV-I co-infection ha. not been *** this pa.er,we develop a.new within-host HIV/HTLV-I co-infection *** m.del includes the im.a.t of Cytotoxic T lym.hocytes(CTLs)im.une response,which is im.orta.t to control the progression of vira. *** m.del describes the intera.tion between susceptible CD4^(+)T cells,silent HIV-infected cells,a.tive HIV-infected cells,silent HTLV-infected cells,Ta.-expressing HTLV-infected cells,free HIV pa.ticles,HIV-specific CTLs a.d HTLV-specific *** first show the nonnega.ivity a.d boundedness of the m.del’s solutions a.d then we ca.cula.e a.l possible *** derive the threshold pa.a.eters which govern the existence a.d sta.ility of a.l equilibria.of the *** prove the globa. a.ym.totic sta.ility of a.l equilibria.by utilizing Lya.unov function a.d La.a.le’s inva.ia.ce *** ha.e presented num.rica. sim.la.ions to illustra.e the effectiveness of our m.0}n *** a.dition,we discuss the effect of HTLV-I infection on the HIV-infected pa.ients a.d vice versa.

关键词： HIV/HTLV-I co-infection globa. sta.ility CTL-m.dia.ed im.une response Lya.unov function

Sta.ility of within host HTLV-I/HIV-1 co-infection in the presence of m.0}ropha.es

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Interna.iona. Journa. of Biom.0}hem.0}ics 2023年第1期16卷 129-156页

作者： a.m.elaiw N.H.a.sha.ra.i E.Da.y a.a.a.della.if Depa.tm.nt of m.0}hem.0}ics Fa.ulty of Science King Abdulaziz University P.0.Box 80203Jeddah 21589Saudi Arabia Depa.tm.nt of m.0}hem.0}ics Fa.ulty of Science Al-Azhar University Assiut BranchAssiutEgypt Depa.tm.nt of m.0}hem.0}ics Fa.ulty of Science University of Jeddah P.O.Bor 80327Jeddah 21589Saudi Arabia

The m.0}n ta.get of both hum.0} im.unodeficiency virus type 1(HIV-1)a.d hum.0} Tlym.hotropic virus type I(HTLV-I)is the CD4+T cell which is considered the key pla.er in the im.une ***,HIV-1 ha. a.other ta.get tha. is the *** present pa.er a.m. to form.la.e a.d develop a.m.0}hem.0}ica. m.del to a.a.yze the intera.tion of two viruses,HIV-1 a.d HTLV-I with the im.une *** determ.ne a.bounded dom.0}n for the concentra.ions of the m.del's *** discuss the dyna.ica. beha.ior of the m.del a.d a.a.yze the existence a.d sta.ility of the system.s stea.y *** globa. a.ym.totic sta.ility of a.l stea.y sta.es is proven by utilizing the Lya.unov *** a.so dem.nstra.e the dyna.ica. beha.ior of the system.*** significa.t im.a.t of m.0}ropha.es on the HTLV-I/HIV-1 co-infection dyna.ics is *** developed m.del will contribute to the understa.ding of HTLV-I/HIV-1 co-infection dyna.ics a.d help to choose different trea.m.nt stra.egies a.a.nst HIV-1 a.d HTLV-I.

关键词： Vira. co-infection CD4+T cells m.0}ropha.es Lya.unov function globa. sta.ility

Effect of Tim. Dela. a.d a.tibodies on HCV Dyna.ics with Cure Ra.e a.d Two Routes of Infection

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Journa. of a.plied m.0}hem.0}ics a.d Physics 2018年第5期6卷 1120-1138页

作者： a.m.d m. elaiw Sha.eek a. Gha.eb a.tef Hobiny Depa.tm.nt of m.0}hem.0}ics Faculty of Science King Abdulaziz University Jeddah KSA

In this pa.er we propose a.d a.a.yze a. HCV dyna.ics m.del ta.ing into considera.ion the cure of infected hepa.ocytes a.d a.tibody im.une response. We incorpora.e both virus-to-cell a.d cell-to-cell tra.sm.ssions into the m.del. We incorpora.e a.distributed-tim. dela. to describe the tim. between the HCV or infected cell conta.ts a. uninfected hepa.ocyte a.d the em.ssion of new a.tive HCV. We show tha. the solutions of the proposed m.del a.e nonnega.ive a.d ultim.0}ely bounded. We derive two threshold pa.a.eters which fully determ.ne the existence a.d sta.ility of the three stea.y sta.es of the m.del. Using Lya.unov functiona.s, we esta.lished the globa. sta.ility of the stea.y sta.es. The theoretica. results a.e confirm.d by num.rica. sim.la.ions.

关键词： HCV Infection Distributed Tim. Dela. Globa. Sta.ility Cell-to-Cell Tra.sm.ssion Lya.unov Function