Salisu Usaini

The problem of kidnapping as a social menace to a society is increasing in some African countries such as Nigeria. We therefore proposed a new deterministic mathematical model for the dynamics of Kidnapping in a community. This menace is considered like a two strains communicable disease with kidnapping propagation mission by kidnappers as one strain and adoption mission for kidnapped victims as the other strain to assess the impact of super-infection. The model exhibits four equilibrium points each of which is unique and asymptotically stable both locally and globally under certain conditions. We obtain the kidnapping propagation number where is the propagation number associated with strain . Another important threshold parameters associated with respective strains 1 and 2 are and . Indeed, we show that at most one strain invades the population if one of these parameters is less than unity. while the two strains coexist at endemic state when both and are greater than unity. The global stability results of the model equilibria are established by numerical simulations. This simulations results indicate that the super-infection destabilizes the coexistence equilibrium.

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.

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.

Some factors related to students behaviour are perceived to be important for academic failure. Such of these factors and some other factors contribute immensely to the problem of scholastic underachievement that is spreading among students of Kano University of Science and Technology, Wudil‐Nigeria. Considering such a problem as a contagious disease, we propose a mathematical model to study how this problem is spread in Kano University of Science and Technology, Wudil campus. The model analysis reveals that the reproduction numbers are sufficient to predict whether the problem can persist in the campus environment. Indeed, endemic persistence occurs if the pattern of recruiting new members is through both transition and progression. The sensitivity analysis of the parameters of the model threshold quantities shows that reducing the rates of recruiting new students to weak class through both transition and progression is an effective measure of containing the problem.