An Analytical SIR model of Epidemics and a Sustainable Suppression Policy: Testing

Why do most simulations using the SIR model of epidemics conclude that the COVID-19 breakout will end up with a significant fraction of the population infected (>60%)? Are there conditions and sustainable policies that can prevent herd immunity? I build an analytical SIR model of epidemics which gives transparent expressions for the disease dynamics and long-run outcomes. I can explicitly solve for conditions that lead to herd immunity, and more importantly, identify other conditions and corresponding policies that prevent it. Infection testing identifies infected individuals and reduces their contact rate, and therefore, reduces the reproduction number of the disease, total infections and even prevents herd immunity. Costs of testing can be kept low if initially sufficiently many tests are conducted. Moreover, other temporary suppression policies become complementary to the sustainable suppression policy - testing - and can reduce total infections over the epidemic.