We use a simple general model of interactive dynamics between the COVID-19 pandemic and the economy to examine the impact of various non-pharmaceutical interventions in the form of restrictions on socio-economic activities like lockdowns, travel restrictions etc. We mathematically demonstrate that these restrictions might be useful in preventing repeated waves of infection recurrence in the pandemic. These results are general and not dependent on choice of specific functional forms or parameter configurations. We set out briefly the implications of these results for public health interventions.