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,

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 equilibrium 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-infection 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 rate of disease avertion when compared to other stratagies. Sensitivity analysis of the parameters as shown in model, shows parameters that have high impact on the chosen classes.

The study of COVID-19 pandemic which paralyzed global economy of countries is a crucial research area for effective future planning against other epidemics. Unfortunately, we now have variants of the disease resulting to what is now known as waves of the pandemic. Several mathematical models have been developed to study this disease. While recent models incorporated control measures, others are without optimal control measures or demographic parameters. In this study, we propose a deterministic compartmental epidemiological model to study the transmission dynamic of the spread of the third wave of the pandemic in Nigeria, and we incorporated optimal control measures as strategies to reduce the burden of the deadly disease. Specifically, we investigated the transmission dynamics of COVID-19 model without demographic features. We then conducted theoretical analysis of the model with and without optimal control strategy. In the model without optimal control, we computed the reproduction number, an epidemiological threshold useful for bringing the third wave of the pandemic under check in Nigeria, and we proofed the disease stability and conducted sensitivity analysis in order to identify parameters that can impact the reproduction number tremendously. In a similar reasoning, for the model with control strategy, we check the necessary condition for the model. To validate our theoretical analyses, we illustrated the applications of the proposed model using COVID-19 data for Nigeria for a period when the country was under the yoke of the third wave of the disease. The data were then fitted to the model, and we derived a predictive tool toward making a forecast for the cumulative number of cases of infection, cumulative number of active cases and the peak of the third wave of the pandemic. From the simulations, it was observed that the presence of optimal control parameters leads to significant impact on the reduction of the spread of the disease. However, it was discovered that the success of the control of the disease relies on the proper and effective implementation of the optimal control strategies efficiently and adequately.

The kernel of the work in this article is the proposition of a model to examine the effect of control measures on the transmission dynamics of Omicron variant of coronavirus disease in the densely populated metropolis of Lagos. Data as relate to the pandemic was gathered as officially released by the Nigerian authority. We make use of this available data of the disease from 1st of December, 2021 to 20th of January, 2022 when omicron variant was first discovered in Nigeria. We computed the basic reproduction number, an epidemiological threshold useful for bringing the disease under check in the aforementioned geographical region of the country. Furthermore, a forecasting tool was derived, for making forecasts for the cumulative number of cases of infection as reported and the number of individuals where the Omicron variant of COVID-19 infection is active for the deadly disease. We carried out numerical simulations of the model using the available data so gathered to show the effects of non-pharmaceutical control measures such as adherence to common social distancing among individuals while in public space, regular use of face masks, personal hygiene using hand sanitizers and periodic washing of hands with soap and pharmaceutical control measures, case detecting via contact tracing occasioning clinical testing of exposed individuals, on the spread of Omicron variant of COVID-19 in the city. The results from the numerical simulations revealed that if detection rate for the infected people can be increased, with majority of the population adequately complying with the safety protocols strictly, then there will be a remarkable reduction in the number of people being afflicted by the scourge of the highly communicable disease in the city.