Corona-virus disease 2019 (COVID-19) is an infectious disease that has affected different groups of humankind such as farmers, soldiers, drivers, educators, students, healthcare workers and many others. The transmission rate of the disease varies from one group to another depending on the contact rate. Healthcare workers are at a high risk of contracting the disease due to the high contact rate with patients. So far, there exists no mathematical model which combines both public control measures (as a parameter) and healthcare workers (as an independent compartment). Combining these two in a given mathematical model is very important because healthcare workers are protected through effective use of personal protective equipment, and control measures help to minimize the spread of COVID-19 in the community. This paper presents a mathematical model named SWE HR; susceptible individuals (S), healthcare workers (W), exposed (E), symptomatic infectious ( ), asymptomatic infectious ( ), hospitalized (H), recovered (R). The value of basic reproduction number for all parameters in this study is 2.8540. In the absence of personal protective equipment and control measure in the public , the value of which implies the presence of the disease. When and were introduced in the model, basic reproduction number is reduced to 0.4606, indicating the absence of disease in the community. Numerical solutions are simulated by using Runge–Kutta fourth-order method. Sensitivity analysis is performed to presents the most significant parameter. Furthermore, identifiability of model parameters is done using the least square method. The results indicated that protection of healthcare workers can be achieved through effective use of personal protective equipment by healthcare workers and minimization of transmission of COVID-19 in the general public by the implementation of control measures. Generally, this paper emphasizes the importance of using protective measures.

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Corruption is a worldwide problem that affects many countries where by individuals loses their rights, lower community confidence in public authorities, absence of peace and security, misallocation of resources and termination of employment. Despite various measures which have been taken by various countries to control corruption, the problem still exists. In this paper, we formulate and analyze a mathematical model for the dynamics of corruption in the presence of control measures. Analysis of the model shows that both Corruption Free Equilibrium (CFE) and Corruption Endemic Equilibrium (CEE) exist. The next generation matrix method was used to compute the effective reproduction number (ܴ ) which is used to study the corruption dynamics. The results indicate that CFE is both locally and globally asymptotically stable when ܴ < 1 whereas CEE is globally asymptotically stable when ܴ > 1. The normalized forward sensitivity method was used to describe the most sensitive parameters for the spread of corruption. The most positive sensitive parameters are κ and ν while the most negative sensitive parameters are α and β . Therefore, the parameters of mass education α and religious teaching β are the best parameters for control of corruption. The model was simulated using Runge-Kutta fourth order method in MATLAB and the results indicate that the combination of mass education and religious teaching is effective to corruption control within short time compared to when each control strategy is used separately. Therefore, this study recommends that more efforts in providing both mass education and religious teaching should be applied at the same time to control corruption.

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