Modelling and Analysis of a Model for Chlamydia Trachomatis Transmission Dynamics

Abstract

Chlamydiainfection,oneofthecommonestsexuallytransmittedinfections(STIs),remaina public healthchallengeinbothunderdevelopedanddevelopedcountriesoftheworld.Chlamydia trachomatis hasbeenobservedtohavenegativehealthconsequenceshencemuchresearchworkis needed tobedonetocurbthespreadofthediseaseinthepopulation.Inthispaper,amathematical model forstudyingtheimpactofcondomusageandtreatmentonthetransmissiondynamicsand control ofChlamydiainthepopulationispresented.Qualitativeanalysisofthemodelshowsthatit undergoes thephenomenonofbackwardbifurcation.Intheabsenceofthisphenomenon(whichis showntooccurasaresultofthereinfectionofrecoveredindividuals),thedisease-freeequilibriumof the modelisgloballyasymptoticallystablewhenevertheassociatedreproductionnumberislessthan unity.Further,forthesamescenarioasabove,itisshownthattheuniqueendemicequilibriumof the modelexistswheneverthereproductionnumberisgreaterthanunity.Numericalresultsshow a relationshipbetweentheprogressionrate,treatmentrateandthereproductionnumber.Results from thesensitivityanalysisofthemodel,usingthereproductionnumber, Rc revealthatthetop parameters thatsigni cantlydrivethedynamicsofChlamydiainthepopulationarethee cacy of condoms,condomcompliance,afractionoftreatedindividualswhorecoverduetoe ective treatment andtreatmentrate.Numericalsimulationsofthemodelsuggestthatinfectedpersons after treatmentshouldwaitforatleast7daysbeforeengaginginanyformofsexualactivityor,if not possibleusecondomscorrectly(toavoidreinfection)inordertoe ectivelycontrolthespread of thediseaseinthepopulation.