This work is aimed at formulating a mathematical model for the transmission dynamics and control of corona virus disease in a population. The Disease Free Equilibrium state of the model was determined and shown to be locally asymptotically stable. The Endemic Equilibrium state of the model was also established and proved to be locally asymptotically stable using the trace and determinant method, after which we determined the basic reproduction number ( ) of the model using the next generation method. When ( ), the disease is wiped out of a population, but if ( ), the disease invades such population. Local sensitivity analysis result shows that the rate at which the exposed are quarantined ( ), the rate at which the infected are isolated ( ), the rate at which the quarantined are isolated ( ), and the treatment rate ( ) should be targeted by the control intervention strategies as an increase in the values of these parameters (  and ) will reduce the basic reproduction number  ( ) of the COVID-19 and as such will eliminate the disease from the population with time. Numerical simulation of the model shows that the disease will be eradicated with time when enlightenment control measure for the susceptible individuals to observe social distance, frequent use of hand sanitizers, covering of mouth when coughing or sneezing are properly observed. Moreso, increasing the rates at which the suspected and confirmed cases of COVID-19 are quarantined and isolated respectively reduce the spread of the global pandemic.

This work is aimed at formulating a mathematical model for the control of zika virus infection using Sterile Insect Technology (SIT). The model is extended to incorporate optimal control strategy by introducing three control measures. The optimal control is aimed at minimizing the number of Exposed human, Infected human and the total number of Mosquitoes in a population and as such reducing contacts between mosquitoes and human, human to human and above all, eliminates the population of Mosquitoes. The Pontryagin’s maximum principle was used to obtain the necessary conditions, find the optimality system of our model and to obtain solution to the control problem. Numerical simulations result shows that; reduction in the number of Exposed human population, Infected human population and reduction in the entire population of Mosquito population is best achieved using the optimal control strategy.