Global Stability Analysis of a Mathematical Model on the Transmission Dynamics of Covid-19 With Vaccination

Abstract

In this work, we investigate the Global Stability of a Mathematical model that describes the impact of vaccination on the dynamics of COVID-19 disease transmission in a human population. The model, represented by a system of ordinary differential equations explains how infection from an index case, which could potentially lead to endemic state, can be averted through effective vaccination. The global stability analysis shows that, the diseases free state is globally asymptotically stable, when the basic reproduction number, in the absence of disease associated death. This is supported by numerical simulation which suggests the combination of vaccination and non-pharmaceutical measures in the disease control. We also show numerically that the disease invades when and that there is a transcritical bifurcation at .

Mathematical modelling and analysis of Kidnapping dynamics

“…+ eventually enter Ω. Therefore it is sufficient to consider the dynamics of system (1) in Ω. Hence the model ( 1) is considered to be mathematically and criminology well possed in Ω.…”

“…This is perhaps, due to terrorism, drug addiction, cultism or gangsterism and the high level of corruption and insecurity in some countries. On this note, Okrinya [1], proposed a simple deterministic mathematical model on kidnapping. The model describes the evolution and propagation of kidnapping as a crime in human society and the model features mimic dynamics of an infectious disease.…”

“…Also, the analysis reveals that reducing the recruitment rate of kidnappers and increasing the rescue rate without any causality on the part of kidnapped victims will lead to eradication of kidnapping in a society. Furthermore, numerical simulation shows that more than half of the population will become kidnapped victims within a period of twenty years whereas 38% of the population would be attracted to the criminal act of kidnapping [1]. In a similar note, Okrinya and Consul extended the model of kidnapping presented in [2] by incorporating de-radicalizing and rehabilitation of kidnappers as preventive measures.…”