COVID-19, an infectious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), starting from Wuhan city of China, plagued the world in the later part of 2019. We developed a deterministic model to study the transmission dynamics of the disease with two categories of the Susceptibles (ie Immigrant Susceptibles and Local Susceptible). The model is shown to have a globally stable disease-free equilibrium point whenever the basic reproduction number is less than unity. The endemic equilibrium is also shown to be globally stable for under some conditions. The spread of the disease is also shown to be highly sensitive to use of PPEs and personal hygiene , transmission probability , average number of contacts of infected person per unit time (day) , the rate at which the exposed develop clinical symptoms and the rate of recovery . Numerical simulation of the model is also done to illustrate the analytical results established.

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The discovery of vaccines for COVID-19 has been helpful in the fight against the spread of the disease. Even with these vaccines, the virus continues to spread in many countries, with some vaccinated persons even reported to have been infected, calling for administration of booster vaccines. The need for continued use of nonpharmaceutical interventions to complement the administration of vaccines cannot therefore be overemphasized. This study presents a novel mathematical model to study the impact of quarantine and double-dose vaccination on the spread of the disease. The local stability analysis of the COVID-19-free and endemic equilibria is examined using the Lyapunov second technique. The equilibria are found to be locally asymptotically stable if R 0 < 1 and R 0 > 1 , respectively. Besides other analytical results, numerical simulations are performed to illustrate the analytical results established in the paper.

A mathematical model is proposed to study the dynamics of the transmission of rabies, incorporating predation of dogs by humans. The model is shown to have a unique disease-free equilibrium which is globally asymptotically stable whenever ℛ0≤1. Local sensitivity analysis suggests that the disease can be controlled through reducing contact with infected dogs, increasing immunization of dogs, screening recruited dogs, culling of infected dogs, and use of dog meat as a delicacy.

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