مدل عفونت HIV - 1 درون ميزبان بر اساس سن با انتقالات سلول به سلول و ويروس به سلول

چكيده انگليسي :

An age structured within host HIV 1 infection model with virus to cell and cell to cell transmissions Mina Kabiri m kabiri@math iut ac ir january 22 2020 Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Rasoul Asheghi r asheghi@iut ac ir2000 MSC 37N25 92B05 37B25Keywords Within host HIV 1 infection age since infection persistence Lyapunov functional LaSalle sinvariance principle stabilityAbstract Introduction to epidemic modeling is usually made through one of the first epidemic models proposed by Kermackand McKendrick in 1927 a model known as the SIR epidemic model and by ignoring the hypotheses of the model SIR we arrive at the complicated SIS and SIR models with demography In these models we saw that the most basic SIRepidemic model has a unique endemic equilibrium which is globally stable if R0 1 This means that every solutionconverges to a stationary state On the other hand many times the incidence or the prevalence data of various diseasesexhibit periodicity To illustrate the application of the Hopf bifurcation theorem we consider a simple modificationof the SIR model Assume that the transmission coefficient of infection is not constant but linear in the number ofdiseases Chronological age is perhaps one of the most important factors distinguishing individuals in a populationthat needs to be incorporated in population and epidemic models Undoubtedly vital characteristics such as birthand death rates differ markedly among individuals of various ages Age is also a key to capturing important mixingpatterns in epidemic models For instance in childhood diseases children predominantly mix with other children insimilar age groups as well as with the individuals of the age groups of their parents and grandparents Children are atthe highest risk for contracting malaria and exhibiting most muscular symptoms and the highest death rate yet malariaaffects all age groups The incidence of HIV is highest in the age groups from age twenty to age forty five Endemicmodels that incorporate births and deaths should also preferably include age structure since with time the age profileof the population may change and that may affect the dynamics of the disease In past decades considerable attentionhas been paid to the within host dynamics of HIV using mathematical modeling Mathematical modeling combinedwith experimental measurements has yielded valuable insights into HIV 1 pathogenesis and has enhanced progress inthe understanding of HIV 1 infection These models mainly investigated the dynamics of the target cells and infectedcells viral production and clearance and the effects of antiretroviral drugs treatment For decades it was believedthat the spreading of HIV 1 within a host was mainly through free circulation of the viral particles with a repeatedprocess However recent studies have revealed that a large number of viral particles can also be transferred frominfected cells to uninfected cells through the formation of virally induced structures termed virological synapses Inthis thesis a within host HIV 1 infection model with virus to cell and direct cell to cell transmission and explicit age since infection structure for infected cells are investigated It is shown that the model demonstrates a global thresholddynamics fully described by the basic reproduction number By analyzing the corresponding characteristic equations the local stability of an infection free steady state and a chronic infection steady state of the model is established Byusing the persistence theory in the infinite dimensional system the uniform persistence of the system is establishedwhen the basic reproduction number is greater than unity Employing suitable Lyapunov functionals and LaSalle sinvariance principle it is shown that if the basic reproduction number is less than unity the infection free steadystate is globally asymptotically stable if the basic reproduction number is

كبيري، مينا

مدل عفونت HIV - 1 درون ميزبان بر اساس سن با انتقالات سلول به سلول و ويروس به سلول

اصل پايايي لاسال , تابع لياپانوف , نقطه تعادل ماندگار , نقطه تعادل بدون بيماري , معادله مشخصه , عدد باز توليد پايه