The history of coronavirus can be traced to the 1960s when B184 and 229E coronaviruses were discovered in the nasal washing of individuals with the common cold. There was no worry about such viruses until 2003 when the first major outbreak of SARS was discovered in southern China. The recent outbreak was in 2019 when a major outbreak of COVID-19 strain started in China. The World Health Organisation proclaimed COVID-19 as a pandemic in March 2020. Ever since this pandemic, several attempts to intervene in the spread has been tried, yet the pandemic is not dying. This persistence in the pandemic might be due to the presence of asymptomatic individuals. This unending pandemic has hit the Kenya economy badly. In this study, we mathematically investigate the effect of governmental and non-governmental intervention on the spread of COVID-19 in Kenya. To capture the effect of intervention effectively, the model considers the presence of asymptomatically infected individuals in the Kenya. The basic reproduction number is obtained using the next-generation matrix and the local stability of the equilibrium points are established. The effects of intervention on the spread of COVID-19 are simulated and illustrated as graphs. The results indicate that intervention in form awareness and public sensitisation reduces the Exposed class, Infected Classes and COVID-19-related death.