A new deterministic mathematical model for the transmission dynamics of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) is proposed and fully analyzed. The presented model exhibits a unique endemic equilibrium and there is no infection free equilibrium due to constant influx of latent immigrants. An invasion threshold parameter is derived and stability analysis of the full model and its two special cases is carried out. The impact of quarantine and isolation is assessed via threshold analysis approach, while the impact of immigration on the disease prevalence is discussed. Indeed, we showed that MERS-CoV can be controlled by quick isolation or monitoring close contacts and quarantining of suspected latent immigrants. Further, numerical simulations of the model reveal that the disease can be contained if these preventive measures are combined with high reduction of immigration rate.

Diphtheria is a severely infectious and deadly bacterial disease with Corynebacterium diphtheriae as the causative agent. Since the COVID-19 pandemic, contagious diseases such as diphtheria have re-emerged due to disruptions in routine childhood immunization programs worldwide. Nigeria is witnessing a significant increase in diphtheria outbreaks likely due to an inadequate health care system and insufficient public enlightenment campaign. This paper presents a mathematical epidemic diphtheria model in Nigeria, which includes a public enlightenment campaign to assess its positive impact on the prevalence of the disease. The mathematical analysis of the model reveals two equilibrium points: the diphtheria infection-free equilibrium and the endemic equilibrium. These equilibrium points are shown to be stable globally asymptotically if ${\mathcal{R}}_c<1$ and ${\mathcal{R}}_c>1$, respectively. The model was fit using the confirmed diphtheria cases data of Kano State from January to December 2023. Sensitivity analysis indicates that the transmission rate and recovery rate of asymptomatic peopleare crucial parameters to be considered in developing effective strategies for diphtheria control and prevention. This analysis also reveals that the implementation of a high-level public enlightenment campaign and its high efficacy effectively reduce the prevalence of diphtheria. Finally, numerical simulations show that combining the public enlightenment campaign and isolating infected individuals is the best strategy to contain the spread of diphtheria.

Hepatitis B is a serious liver infection caused by hepatitis B virus (HBV). In this paper, we review the deterministic model of HBV proposed by Emerenini and Inyama in 2018 to carry out a rigorous mathematical analysis. The analysis of the model reveals that an endemic equilibrium exists in addition to the disease free equilibrium (DFE) point. The vaccinated reproduction number, Rv is derived and revealed that if Rv < 1, the DFE is locally asymptotically stable and is unstable when Rv > 1, while the endemic equilibrium point (EEP) is the only asymptotic stable equilibrium point when Rv > 1. The global asymptotic stability of both the disease free equilibrium and endemic equilibrium points are proved using Lyapunov function in conjunction with LaSalles’ Invariance Principle. Furthermore, we obtain the minimum value of the fraction of newborn babies required to be vaccinated for effective disease control.