No test is better than a bad test"": Impact of diagnostic uncertainty in mass testing on the spread of Covid-19

Nicholas Gray; Dominic Calleja; Alex Wimbush; Enrique Miralles-Dolz; Ander Gray; Marco De-Angelis; Elfride Derrer-Merk; Bright Uchenna Oparaji; Vladimir Stepanov; Louis Clearkin; Scott Ferson

The SIR model used in this paper uses discrete-time binomial sampling for calculating movements of individuals between states. For a defined testing strategy, with an active viral test having sensitivity, specificity and capacity of σ A , τ A and C A respectively, an antibody test with sensitivity, specificity and capacity σ B , τ B and C B respectively and a testing prevalence of p, these rates are defined as follows: N A = min (C A , Bin (S + I, ρ)) , (6a) N B = min (C B , Bin (Q S + Q R , φ)) , (6b) T I = min (N A p, Ip) , (6c) T S = min(S, N A − T I ), (6d) At each time step t, the model calculates the number of persons moving between each state in the order defined above. The use of a binomial model was prompted by a desire to incorporate both aleatory and epistemic uncertainty in each movement. The current approach does not make use of epistemic uncertainty, fixing the model parameters σ A , τ A , σ B , τ B , φ, ρ, C A , C B and p. A discrete time model was selected to allow for comparisons against available published data detailing recorded cases and recoveries on a day-by-day basis.