Background: Mobility restrictions prevent the spread of infections to disease-free areas, and early in the coronavirus disease 2019 (COVID-19) pandemic, most countries imposed severe restrictions on mobility as soon as it was clear that containment of local outbreaks was insufficient to control spread. These restrictions have adverse impacts on the economy and other aspects of human health, and it is important to quantify their impact for evaluating their future value. Methods: Here we develop Scotland Coronavirus transmission Model (SCoVMod), a model for COVID-19 in Scotland, which presents unusual challenges because of its diverse geography and population conditions. Our fitted model captures spatio-temporal patterns of mortality in the first phase of the epidemic to a fine geographical scale. Results: We find that lockdown restrictions reduced transmission rates down to an estimated 12\% of its pre-lockdown rate. We show that, while the timing of COVID-19 restrictions influences the role of the transmission rate on the number of COVID-related deaths, early reduction in long distance movements does not. However, poor health associated with deprivation has a considerable association with mortality; the Council Area (CA) with the greatest health-related deprivation was found to have a mortality rate 2.45 times greater than the CA with the lowest health-related deprivation considering all deaths occurring outside of carehomes. Conclusions: We find that in even an early epidemic with poor case ascertainment, a useful spatially explicit model can be fit with meaningful parameters based on the spatio-temporal distribution of death counts. Our simple approach is useful to strategically examine trade-offs between travel related restrictions and physical distancing, and the effect of deprivation-related factors on outcomes.