We investigated the intracellular delay effect on the stability of the endemically infected steady state by analyzing a nonlinear ordinary differential equation model of hepatitis B virus (HBV) infection that considers the interaction betweena replicating virus, hepatocytes and the cytotoxic T lymphocytes (CTL). We gave a criterion to ensure that the infected steady state is asymptotically stable for all delays. A critical delay below which the CTL (immune control mechanism) can be significantly helpful in controlling the HBV infection even when the basic reproduction number is high is allowed in the analysis.

In this model we study the dynamics and control of hepatitis B virus (HBV) infection which is a major health problem worldwide by considering condom, vaccination and treatment as control measures. Initially we determined the basic reproduction number R_0 for the model and observe that once R_0<1, the disease free equilibrium will be stable and HBV infection can be controlled using the three control measures and we also study the solution of the endemic equilibrium point of the model. Next we take the sensitivity analysis of the basic reproduction number of HBV infection and obtain that the endemicity of the infection will reduce with the controls. Finally, the numerical simulation result shows that combination of condom, vaccination and treatment is the most effective way to control hepatitis B infection.

Stakeholder management is the process of identifying, analyzing, and engaging people who have either positive or negative influence in a project. The people involved in any project are called stakeholders and all projects have stakeholders irrespective of the size. Managing these stakeholders is a major function of project managers especially the most important ones because their action will determine whether the project is successful or not. Literatures have outlined different strategies of managing stakeholders which lies around stakeholder identification. This paper formulated mathematical model to determine the most important variable in managing stakeholders. In conclusion, the carrying capacity of a project should be considered alongside other stakeholder management strategies like active listening to bring the project to a successful completion.

We proposed and solved a combined control malaria system of fifteen ordinary differential equations modeling the transmission dynamics of malaria between humans and mosquitoes. Since our aim is to minimize the number of exposed and infectious human, we discussed the disease free equilibrium and estimated the basic reproduction number using the next generation matrix method. The disease free equilibrium was asymptotically stable when the reproduction number is less than one and unstable when it is greater than one. Numerical results are provided using matlab software to confirm the analyzed results. Our findings were that malaria may be controlled using the combined control method, the insecticide treated bed nets, fumigation of the surroundings and active malaria drug as this will reduce the contact rate between human and mosquito through reduction in mosquito population and malaria transmission.

Malware remains a significant threat to computer network.  In this paper, we consideredthe problem which computer malware cause to personal computers with its control by proposing a compartmental model SVEIRS (Susceptible Vaccinated-Exposed-infected-Recovered-Susceptible) for malware transmission in computer network using nonlinear ordinary differential equation. Through the analysis of the model, the basic reproduction number  were obtained, and the malware free equilibrium was proved to be locally asymptotical stable if  is less than unity and globally asymptotically stable if Ro is less than some threshold using a Lyapunov function. Also, the unique endemic equilibrium exists under certain conditions and the model underwent backward bifurcation phenomenon. To illustrate our theoretical analysis, some numerical simulation of the system was performed with RungeKutta fourth order (KR4) method in Mathlab. This was used in analyzing the behavior of different compartments of the model and the results showed that vaccination and treatment is very essential for malware control.