COVID-19 national spikes had been reported at varying temporal scales as a result of differences in the driving factors. Factors affecting case load and mortality rates have varied between countries and regions. We investigated the association between various socio-economic, demographic and health variables with the spread on COVID-19 cases in Eswatini using the maximum likelihood estimation method for count data. A generalized Poisson regression (GPR) model was fitted with the data comprising of fifteen covariates to predict COVID-19 risk in Eswatini. The results showed that variables that were key determinants in the spread of the disease were those that included the proportion of elderly above 55 years at 98% (95% CI: 97%-99%) and the proportion of youth below 35 years at 0.08% (95% CI: 0.017%-38%) with a pseudo R-square of 0.72. However, in the early phase of the virus when cases were fewer, results from the Poisson regression showed that household size, household density and poverty index were associated with COVID-19. We produced a risk map of predicted COVID-19 in Eswatini using the variables that were selected at 5% significance level. The map could be used by the country to plan and prioritize health interventions against COVID-19. The identified areas of high risk may be further investigated in order to find out the risk amplifiers and assess what could be done to prevent them.