We construct a simple mathematical model that describes the dynamics of the transmission of COVID-19 disease in a human population. It accounts for the various phases of the disease and its mode of contact through infectious humans and surfaces. The contribution of asymptomatic humans in the dynamics of the disease is well represented. The model is a system of ordinary dierential equations that describes the evolution of humans in a range of COVID-19 states due to emergence of an index case. The analysis includes establishment of the basic reproduction number, R0, where, R0 < 1 signifies a disease free state that is locally asymptotically stable. A key result in this study shows some long term damped oscillatory behaviour that do not seem to end soon.

We construct a Mathematical model that describes the effect of vaccination on the dynamics of the transmission of COVID-19 disease in a human population. The model is a system of ordinary differential equations that describes the evolution of humans in a range of Covid-19 states due to emergence of an index case in a disease free region. The analysis of the model shows that effective vaccination can lead to disease eradication, where in the disease free state is locally asymptomatically stable if the basic reproductive number, and unstable when The numerical simulations suggests the use of other social measures alongside  vaccination in order to avert the possibility of the disease  becoming endemic.

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 .

Climatic characteristics involving weather conditions affect malaria transmission in most deltaic regions of the world. Here, we propose a simple mosquito-human interaction model incorporating features of seasonal malaria pathogenesis. We obtain the basic reproduction number and show in our analysis some conditions for local and global stability of the solution, suggesting that intervention strategies should be targeted at reducing seasonal contacts of mosquitoes and humans. The model simulations compare well with malaria infection data.