Optimal COVID-19 epidemic control until vaccine deployment

Ramses Djidjou-Demasse; Yannis Michalakis; Marc Choisy; Micea T. Sofonea; Samuel Alizon

where c is the percentage of reduction in transmission due to public health measures at time t, and β A and β I are the transmission rates of symptomatic and asymptomatic infections respectively. Parameter ξ is the factor of reduction of the transmission rate of severe and symptomatic infections, which is due to being in a health care facility. A proportion p of exposed individuals (λS) move to the mild asymptomatic infection class at a rate ε, while the remainder (1 − p) move to the severe asymptomatic infection class at the same rate ε. We also assume that the epidemic is sustained by migration of E m and E s individuals at a constant rate pν and (1 − p)ν respectively. Severe and mild asymptomatic infectious individuals become symptomatic at a same rate σ and recover at rates γ s and γ m respectively. While mild infections are never lethal, severe cases lead to death at rate α. We assume that the number of severely infected hosts at a given time, I s , affects the disease induced mortality rate (if hospitals are saturated for instance). If we denote by I the total number of infected hosts the health care system (especially the intensive care units, ICU) can sustain, then we assume the mortality rate α to be a step function such that