Mathematical Models for the Spread and Control of Foot‐and‐Mouth Disease During the 1973 Epidemic in Austria

Abstract

Two models are studied to describe the spread of foot-and-mouth disease during the 1973 epidemic in Austria. The models are modifications of a three-class-model (due to KEEMACK and MCKENDRICK) taking into account the special character of the disease 88 well a8 control methods (stamping-out-method, vaccination programs).

Data‐Driven Models of Foot‐and‐Mouth Disease Dynamics: A Review

“…Some models are quantified with host data at a resolution appropriate for modelling targeted control; however, locations using host data are largely limited to Australia (Pech and Hone, ; Garner and Lack, ,b; Dexter, ; Doran and Laffan, ), Europe (Haydon et al., ; Ferguson et al., ,b; Keeling et al., ; Kao, ; Ap Dewi et al., ; Tildesley et al., ; Kao et al., ) and the United States (Bates et al., ,b; Carpenter et al., , ; Ward et al., , ; Highfield et al., ; Tildesley et al., ). Only a subset of models directly incorporates disease data (Klaring and Timischl, ; Woolhouse et al., , ; Haydon et al., ; Howard and Donnelly, ; Ferguson et al., ,b; Keeling et al., ; Gerbier et al., ; Bouma et al., ; Rivas et al., ; Tsutsui et al., ; Gilbert et al., ; Chowell et al., ; Diggle, ; van den Broek and Heesterbeek, ; Chis Ster and Ferguson, ; Savill et al., ; Estrada et al., ; Tildesley et al., ; Chis Ster et al., , ; Jewell et al., ; Boender et al., ; Deardon et al., , ; Lawson et al., ; Hosseinkashi et al., ; Vergne et al., ); of this subset, the UK 2001 outbreak is overrepresented. Overall, models appropriate for targeted control represent areas where current infections with FMDV are not observed and locations with high FMD incidence are not represented in the modelling literature.…”

“…The first models, presented in 1760, address the use of vaccinations to control smallpox (Bernoulli, ; Dietz and Heesterbeek, ), and later models established general theory of outbreaks (Ross, ; Kermack and McKendrick, ; Klepac et al., ). By the mid‐20th century, models of FMDV transmission and control appeared in the literature (Hughjones, ; Klaring and Timischl, ). Generally, transmission models categorize individuals by disease status; for FMDV transmission, the SEIR model denotes animals as susceptible (S) to FMDV, exposed (E) or infected but not yet infectious, infected (I) and infectious, and recovered or removed (R) from chains of transmission (Anderson and May, ; Keeling and Rohani, ).…”