Optimal control of Chlamydia model with vaccination

Abstract

This paper presents an SVEIRT epidemiological model in the human population with Chlamydia trachomatis. The model incorporated the vaccination class and investigated the role played by some control strategies in the dynamics of the disease (Chlamydia tracomatis). The reproduction number which helps in determining the rate of spread of the disease, was calculated using the method proosed by van den Driessche and Watmough.The local and global stability of the equlibrium points where established, where it was observed that the model is locally asymptotically stable if the reproduction number is less than unity, and globally stable if a certain threshold value is greater than unity or the re-nfection rate is zero. The effect of the re-infection rate on the global stability suggests the exhibition of the phenomenon of backward bifurcation of the model. The backward bifurcation of the system was later studied, and it shows that backward bifurcation will occur if the value of the bifurcation parameter 'a' is positive. The optimal control of the model shows the effect of different strategies in the transmission dynamicsof the disease and the cost effectivenes of each control pair. It was observed that the treatment and control effort gives the most cost effective combinations and at the same time the highest a,b,

Role of fractional derivatives in the mathematical modeling of the transmission of Chlamydia in the United States from 1989 to 2019

“…Here we define the structure of sexually transmitted disease chlamydia in United states using the mathematical model derived by Odionyenma et al [ 6 ]. The population size of the humans is considered into six compartments; unvaccinated susceptible individuals S ( t ), vaccinated susceptible individuals V ( t ), exposed peoples E ( t ), infectious peoples I ( t ), treated humans T ( t ), and humans with recovery R ( t ).…”

“…The authors in Ref. [ 6 ] were defined as an optimal control derivation for the Chlamydia modeling. In [ 7 ], an optimal control modeling of the chronic Chlamydia trachomatis disease considering a combination treatment with tryptophan and antibiotic was derived.…”

Analysis of COVID‐19 and comorbidity co‐infection model with optimal control

“…24,25 Mathematical modeling has been a powerful means of studying the behaviour of infectious diseases. [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] A lot of models have been developed for the dynamics of COVID-19. [41][42][43][44][45] For instance, the authors in Reference 44 developed and analyzed a mathematical model for COVID-19 population dynamics in Lagos, Nigeria.…”

“…Mathematical modeling has been a powerful means of studying the behaviour of infectious diseases 26‐40 . A lot of models have been developed for the dynamics of COVID‐19 41‐45 .…”

“…2 As of February 19, 2021, the global cases of COVID-19 infection stands at 110,430,962 with 2,444,074 deaths. 3 The morbidity and mortality vary across countries of the world with the highest reported in the United States (27,897,356 confirmed cases with 493,138 deaths), India (10,963,394 confirmed cases with 156,111 deaths), and Brazil (10,030,626 confirmed cases with 243,457 deaths) as of February 19, 2021. 3 COVID-19 "can often present as a common cold-like illness," with other symptoms including fever, fatigue, muscle pains, loss or change of taste or smell, shortness of breath, dry cough, and sore throat.…”