As every country in the world struggles with the ongoing COVID-19 pandemic, it is essential that as many people as possible understand the epidemic containment, elimination and exclusion strategies required to tackle it. Simplified arithmetic models of COVID-19 transmission, control and elimination are presented in user-friendly Shiny and Excel formats that allow non-specialists to explore, query, critique and understand the containment decisions facing their country and the world at large. Although the predictive model is broadly applicable, the simulations presented are based on parameter values representative of the United Republic of Tanzania, which is still early enough in its epidemic cycle and response to avert a national catastrophe. The predictions of these models illustrate (1) why ambitious lock-down interventions to crush the curve represent the only realistic way for individual countries to contain their national-level epidemics before they turn into outright catastrophes, (2) why these need to be implemented so early, so stringently and for such extended periods, (3) why high prevalence of other pathogens causing similar symptoms to mild COVID-19 precludes the use of contact tracing as a substitute for lock down interventions to contain and eliminate epidemics, (4) why partial containment strategies intended to merely flatten the curve, by maintaining epidemics at manageably low levels, are grossly unrealistic, and (5) why local elimination may only be sustained after lock down ends if imported cases are comprehensively excluded, so international co-operation to conditionally re-open trade and travel between countries certified as free of COVID-19 represents the best strategy for motivating progress towards pandemic eradication at global level. The three sequential goals that every country needs to emphatically embrace are contain, eliminate and exclude. As recently emphasized by the World Health Organization, success will require widespread genuine national unity and unprecedented global solidarity.