A co-infection model for HPV and syphilis with optimal control and cost-effectiveriess analysis

A co-infection model for human papillomavirus(HPV)and syphilis with cost-effectiveness optimal control analysis is developed and presented.The full co-infectionmodel is shown to undergo the phenomenon of backward bifurcation when a certain con-dition is satisfied.The global asymptotic stability of the disease-free equilibrium of thefull model is shown not to exist when the associated reproduction number is less thanunity.The existence of endemic equilibrium of the syphilis-only sub-model is shown toexist and the global asymptotic stability of the disease-free and endemic equilibria of thesyphilis-only sub-model was established,for a special case.Sensitivity analysis is alsocarried out on the parameters of the model.Using the syphilis associated reproductionnumber,R_(0s),as the response function,it is observed that the five-ranked parametersthat drive the dynamics of the co-infection model are the demographic parameter μ,the efective contact rate for syphilis transmission,β_(s),the progression rate to late stage ofsyphilis σ2,and syphilis treatment rates:τ1 and τ2 for co-infected individuals in com-partments Hi and Hl,respectively.Moreover,when the HPV associated reproductionnumber,R0h,is used as the response function,the five most dominant parameters thatdrive the dynamics of the model are the demographic parameter μ,the effective contactrate for HPV transinission,β_(h),the fraction of HPV infected who develop persistent HPV p1,the fraction of individuals vaccinated against incident HPV infection φ and the HPVvaccine eflicacy πh.Numerical simulations of the optimal control model showed that theoptimal control strategy which implements syphilis treatment controls for singly infectedindividuals is the most cost-effective of all the control strategies in reducing the burdenof HPV and syphilis co-infections.

Mathematical analysis of a tuberculosis model with imperfect vaccine

Since 1921,the Bacille Calmette Guerin(BCG)vaccine continues to be the most widely used vaccine for the prevention of Tuberculosis(TB).However,the immunity induced by BCG wanes out after some time making the vaccinated individual susceptible to TB infection.In this work,we formulate a mathematical model that incorporates the vaccination of newly born children and older susceptible individuals in the transmission dynamics of TB in a population,with a vaccine that can confer protection on older susceptible individuals.In the absence of disease-induced deaths,the model is shown to undergo the phenomenon of backward bifurcation where a stable disease-free equilibrium(DFE)co-exists with a stable positive(endemic)equilibrium when the associated repro-duction number is less than unity.It is shown that this phenomenon does not exist in the absence of imperfect vaccine,exogenous reinfection,and reinfection of prev iously treated individuals.It is further shown that a special case of the model has a unique endemic equilibrium point(EEP),which is globally asymptotically stable when the associated reproduction number exceeds unity.Uncertainty and sensitivity analysis are carried out to identify key parameters that have the greatest infuence on the transmission dynamics of TB in the population using the total population of latently infected individuals,total number of actively infected individuals,disease incidence,and the effective reproduc-tion number as output responses.The analysis shows that the top five parameters of the model that have the greatest influence on the effective reproduction number of the model are the transmission rate,the fraction of fast disease progression,modification parame-ter which accounts for reduced likelihood to infection by vaccinated individuals due to imperfect vaccine,rate of progression from latent to active TB,and the treatment rate of actively infected individuals,with other key parameters infuencing the outcomes of the other output responses.Numerical simulations suggest that with higher vaccination rate of older susceptible individuals,fewer new born children need to be vaccinated,in order to achieve disease eradication.

Mathematical analysis of a two-sex Human Papillomavirus (HPV)model

A two-sex deterministic model for Human Papillomavirus (HPV)that assesses the impact of treatment and vaccination on its transmission dynamics is designed and rigor- ously analyzed.The model is shown to exhibit the phenomenon of backward bifurcation, caused by the imperfect vaccine as well as the re-infection of individuals who recover from a previous infection,when the associated reproduction number is less than unity. Analysis of the reproduction number reveals that the impact of treatment on effective control of the disease is conditional,and depends on the sign of a certain threshold unlike when preventive measures are implemented (i.e.condom use and vaccination of both males and females).Numerical simulations of the model showed that,based on the parameter values used therein,a vaccine (with 75%efficacy)for male population with about 40%condom compliance by females will result in a significant reduction in the disease burden in the population.Also,the numerical simulations of the model reveal that with 70%condom compliance by the male population,administering female vaccine (with 45%efficacy)is sufficient for effective control of the disease.