Dynamics of epidemic diseases without guaranteed immunity

The global SARS-CoV-2 pandemic suggests a novel type of disease spread dynamics. WHO states that there is currently no evidence that people who have recovered from COVID-19 and have antibodies are immune from a second infection [WHO]. Conventional mathematical models consider cases for which a recovered individual either becomes susceptible again or develops an immunity. Here, we study the case where infected agents recover and only develop immunity if they are continuously infected for some time. Otherwise, they become susceptible again. We show that field theory bounds the peak of the infectious rate. Consequently, the theory's phases characterise the disease dynamics: (i) a pandemic phase and (ii) a response regime. The model excellently describes the epidemic spread of the SARS-CoV-2 outbreak in the city of Wuhan, China. We find that only 30% of the recovered agents have developed an immunity. We anticipate our paper to influence the decision making upon balancing the economic impact and the pandemic impact on society. As long as disease controlling measures keep the disease dynamics in the "response regime", a pandemic escalation ('second wave') is ruled out.