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We present a population-based System Dynamics Model (SDM) of possible Covid-19 trajectories under various intervention options in the uniqueness of Kenya. We developed a stock and flow based SDM. We parametrized the SDM using published data and where data was not available, expert opinion was sought. Following validation test, the model was simulated to determined possible outcomes of non-pharmaceutical interventions in management of Covid-19. We simulate the possible impact of; social distancing, quarantining, curfew and cross-county travel restriction, lockdown of selected cities in Kenya and quarantining. We varied interventions in terms of start dates, duration of implementation and effectiveness of the interventions. We estimated the outcomes in terms of number of possible infections, recoveries and deaths. With the current state of interventions, we estimated a peak of Covid-19 in September 2020 with an estimated 13.5 Million Covid-19 cases and 33.8 thousand deaths in Kenya. The largest possible reduction in infections and mortality was achievable through increase in the effectiveness of the interventions. The suggested interventions would delay the epidemic peak of Covid-19 to between late Nov 2020 and early December 2020 with an estimated13M cases a 500 thousand reduction in Covid-19 cases and 32.4 deaths (a reduction in 1400 deaths). We conclude that SDM enables understanding of the complexity and impact of different interventions scenarios of Covid-19 in Kenya.