Tuberculosis has continued to retain its title as "the captain among these men of death". This is evident as it is the leading cause of death globally from a single infectious agent. TB as it is fondly called has become a major threat to the achievement of the sustainable development goals (SDG) and hence require inputs from different research disciplines. This work presents a mathematical model of tuberculosis. A compartmental model of seven classes was used in the model formulation comprising of the susceptible S, vaccinated V, exposed E, undiagnosed infectious I1, diagnosed infectious I2, treated T and recovered R. The stability analysis of the model was established as well as the condition for the model to undergo backward bifurcation. With the existence of backward bifurcation, keeping the basic reproduction number less than unity [Formula: see text] is no more sufficient to keep TB out of the community. Hence, it is shown by the analysis that vaccination program, diagnosis and treatment helps to control the TB dynamics. In furtherance to that, it is shown that preference should be given to diagnosis over treatment as diagnosis precedes treatment. It is as well shown that at lower vaccination rate (0-20%), TB would still be endemic in the population. As such, high vaccination rate is required to send TB out of the community.
With the recent trend in the spread of coronavirus disease 2019 (Covid-19), there is a need for an accurate approximate analytical solution from which several intrinsic features of COVID-19 dynamics can be extracted. This study proposes a time-fractional model for the SEIR COVID-19 mathematical model to predict the trend of COVID-19 epidemic in China. The efficient approximate analytical solution of multistage optimal homotopy asymptotic method (MOHAM) is used to solve the model for a closed-form series solution and mathematical representation of COVID-19 model which is indeed a field where MOHAM has not been applied. The equilibrium points and basic reproduction number ( R 0 ) are obtained and the local stability analysis is carried out on the model. The behaviour of the pandemic is studied based on the data obtained from the World Health Organization. We show on tables and graphs the performance, behaviour, and mathematical representation of the various fractional-order of the model. The study aimed to expand the application areas of fractional-order analysis. The results indicate that the infected class decreases gradually until 14 October 2021, and it will still decrease slightly if people are being vaccinated. Lastly, we carried out the implementation using Maple software 2021a.