Reinfection of a recovered individual either as a result of relapse or new contact no doubt poses a major threat to the eradication of an infection within the host community. In this work, the role of re-infection in the transmission dynamics of COVID-19 was considered and analysed using the semi-analytical tool Differential Transform Method (DTM). COVID-19 (also known as Coronavirus) has shut down the economy of the world since it became a global pandemic. A mathematical model was constructed with consideration of multiple pathways of infection transmission, the treatment strategies and policies adopted (social distancing, wearing of face mask and so on) to limit the spread of the infection globally. The non-linear system of equations governing the model was solved using DTM and the resulting series solution was compared with the standard numeric Runge-Kutta order 4 (RK4). It was discovered that re-integration of a recovered individual into the susceptible community without observing the prevention guidelines such as social distancing, washing of hands and proper sanitizing could increase the spread of the infection since the recovered individuals are not guaranteed of immunity against the infection after recovery. The study concluded that families of recovered patients must ensure adequate preventive measure while integrating their recovered loved ones back to their midst.

COVID-19 became a household name globally in the year 2020 after it was first discovered in Wuhan, China in December 2019. It is a global pandemic that shut the economy of all nations in the larger part of year 2020 by forcing a compulsory holiday on mankind due to its threat of mass death. The menace of this pandemic was combated with the total arsenal in human capacity. One of such weapons is case detection that leads to either self-isolation or quarantine. This weapon helps to reduce the number of new cases that may arise from undetected asymptomatic/symptomatic carriers within a population. In this article, the dynamics of COVID-19 transmission were studied by developing a mathematical model incorporating case detection, the impact of sensitization, and role of early diagnosis in curbing the spread of this disease. The basic properties in terms of existence, uniqueness, and boundedness of solution for the formulated model were discussed. Also, the model was found to exhibit two equilibrium states which are categorised as the disease-free (DFE) and pandemic equilibrium states. The reproductive number for the model was computed and used to establish the stability analysis for both equilibrium states. Center manifold theory was employed to assess the bifurcation analysis of the model and the result shows that the model exhibits forward bifurcation when the reproductive number is greater than and equal to 1.

Cardiovascular diseases (CVDs) have remained the leading causes of global death in the last 16 years which is the cause of mortality of 17.7 million people every year. Nowadays, people live in a time where sitting takes up the majority of their daily affairs. The sedentary behavior for prolonged periods of time can leads to a problem of deadly disease such as heart disease, obesity, and diabetes. In this paper a deterministic model for the effects of prolonged sitting is designed. The model, which consists of three ordinary differentials equations is developed and analyzed to study the optimal control analysis on sedentary behavior, physical activity in relation to cardiovascular disease (CVD) in a community. The solutions of the model uniquely exist, nonnegative for all t ≥ 0 with nonnegative initial conditions in R 3 + , and bounded in a region Ω N . The basic reproduction number which measures the relationship threshold is presented. The model was extended and optimal control theory was applied to examine optimal strategies for controlling or eradicating the new cases of CVD that may be borne due to a life of inactivity. The control measures comprises of education or sensitization u 1 , living a healthy lifestyle (good nutrition, weight management) u 2 , and getting plenty of physical activity u 3 . The impact of using possible combinations of the three intervention strategies was investigated and analyzed. The results of the optimal control model using Pontryagin maximum principle (PMP) revealed that combination of education or sensitization with any other control strategy yields better result to reduce or eradicate the risk of new cases of CVD from sedentary lifestyle.

A general SIQRM epidemic model with vaccination and relapse possibility is proposed for analysis in this work. The idea behind the proposed model is to check the effect of immunity obtained from vaccine or treatment, quarantine effect as well as waning effect of immunity on the transmission rate of Tuberculosis within a population that is subjected to proper education without restricted access. Some other infectious diseases in this category include measles and Ebola. Two equilibrium states of the proposed model are obtained as well as the effective reproduction number(Reff). Stability analysis of the model at the Infection Free Equilibrium(I.F.E) state is established on the condition that Reff<1. Numerical simulation for the general SIQRM model was done using specific data for Tuberculosis disease and the result shows that proper education, vaccination and early diagnosis of an infectious individual for quarantining is an efficient way by which the spread of Tuberculosis can be reduced in the population while adequate medical attention yield better result for detected cases