Description of the mathematical models with their key quantitative results.
Supplementary Table 3 is also available in Excel format here.
| Model category | Original model reference | Spatially explicit | Inference method | Dog population structure | Quantitative results | Outcome in sensitivity analysis | Key parameters in sensitivity analysis | Optimal control strategy | Reference |
|---|---|---|---|---|---|---|---|---|---|
| Deterministic compartmental | Anderson et al., 1991 | NO | Regression | R, critical vaccination coverage | Coleman & Dye, 1996 | ||||
| Fuzzy compartmental | NO | Simulation | Ortega et al., 2000 | ||||||
| Deterministic compartmental | Anderson et al., 1980 | NO | Simulation | R | Annual dog vaccination with 70% coverage or biannual dog vaccination with a 60% coverage | Kitala et al., 2002 | |||
| Deterministic compartmental | NO | Simulation | Characteristic period and damping time of oscillations | Rabies dynamics | Robust | Hampson et al., 2007 | |||
| Deterministic compartmental |
Hampson et al., 2017 Kitala et al., 2002 Coleman et al. 2004 |
NO | Maximum likelihood | Re, weekly numbers of rabid-dog cases for the whole city, human exposures, dog-to-dog transmission rate, dog-to-human transmission rate, number of exposed dogs | Rabies dynamics |
Rabies-related mortality rate, dog-to-dog transmission rate, probability of clinical outcome ++ Carrying capacity, initial number of dogs per km2 + |
70% dog vaccination coverage | Zinsstag et al., 2009 | |
| Deterministic compartmental |
Anderson et al., 1981 Smith & Cheeseman, 2002 Hampson et al., 2007 |
NO | Simulation | Time to eradication | Rabies eradication | Robust when vaccination and fertility control are implemented | = 50% dog vaccination and fertility control coverage | Carroll et al., 2010 | |
| Deterministic compartmental | NO | Simulation | R | R | Dog-to-dog-transmission rate, birth rate, vaccination coverage | Dog population management and dog vaccination | Zhang et al., 2011 | ||
| Stochastic metapopulation | YES | Simulation | Beyer et al., 2011 | ||||||
| Deterministic compartmental | NO | Simulation | Domestic, stray | R | R | Rate at which rabid domestic dogs become rabid stray dogs | 75% dog vaccination coverage and stray dog management | Hou et al., 2012 | |
| Deterministic compartmental | Zhang et al., 2011 | NO | Least-square fitting | R | R | Vaccination coverage, birth rate, baseline contact rate | Dog population management, dog vaccination and public awareness | Zhang et al., 2012 | |
| Stochastic compartmental | NO | MCMC | R, transmission rates, critical level of vaccine coverage | 70% dog vaccination coverage | Fitzpatrick et al., 2012 | ||||
| Stochastic metapopulation | Beyer et al., 2011 | YES | Simulation | Allocation strategies efficacy | Rabies dynamics | Robust to distances among villages | Frequent dog vaccination campaigns targeting the reduction in metapopulation risk | Beyer et al., 2012 | |
| Stochastic agent-based | NO | Maximum likelihood | R, vaccination coverage | Rabies eradication | R, vaccination coverage | Dog vaccination coverage targeting even and 70% coverage | Townsend et al., 2013 | ||
| Stochastic branching process | NO | Simulation | Reactive dog vaccination with rapid surveillance system followed by a 2-year monitoring period | Townsend et al., 2013 | |||||
| Stochastic agent-based | YES | Simulation | R | Outbreak duration, number of rabid dogs | Incubation period, transmission probability given a bite, distance jernel, bite probability given a contact, vaccine efficacy, index community, delay in starting the control strategy of movement restrictions between communities | Reactive dog vaccination until all targeted dogs are vaccinated | Dürr et al., 2015 | ||
| Stochastic agent-based | NO | Simulation | Rc, time to elimination | Rabies elimination | R, number of offspring cases, mean generation interval | Dog vaccination targeting even coverage | Ferguson et al., 2015 | ||
| Deterministic metapopulation | Zhang, 2011 | YES | Simulation | Two-patch R, isolated R | R | Mobility rate | Chen et al., 2015 | ||
| Deterministic compartmental | NO | Simulation | Island and peri-urban free-roaming, wild | Time to detection | Rabies dynamics | Contact rate, incubation period, transmission rate | 90% dog vaccination coverage | Sparkes et al., 2016 | |
| Deterministic compartmental | NO | Simulation | Stray, owned free-roaming, owned confined | Rabies elimination | Dog population size and composition, vaccination coverage per dog subpopulation | Stray dog vaccination coverage should be based on dog population composition | Leung et al., 2017 | ||
| Stochastic agent-based | YES | Simulation | Outbreak size, duration and probability | Network construction parameter, infectious period, incubation period, vaccination coverage | Targeted dog vaccination based on their social and roaming behaviors, public awareness, locally reactive interventions and reporting of 60% of cases by the surveillance system | Laager et al., 2018 | |||
| Stochastic agent-based | Townsend et al., 2013 | YES | Simulation | Stray, confined | Parameter of the influence of dog population density on secondary case locations, mean outbreak sizes under 50% vaccination coverage, mean epidemic durations | Outbreak size | Probability of unintentional release of rabid dogs by their owner, vaccination coverage, probability that a rabid stray dog selects a stray dog to bite | Dog owner awareness besides dog registration, capture of free-roaming dogs, mandatory dog vaccination and quarantine of imported animals | Kadowaki et al., 2018 |
| Deterministic metapopulation |
Zinsstag et al., 2009 Zinsstag et al., 2017 |
YES | Least-square fitting | Time to elimination, averted cases | Outbreak size | Rabies-related mortality rate, incubation period | Laager et al., 2019 | ||
| Stochastic network | Epimodel | YES | Simulation | Network metrics | Wilson-Aggarwal et al., 2019 | ||||
| Stochastic compartmental | Fitzpatrick et al., 2014 | NO | MCMC | Carrying capacities, dog-to-dog transmission rates, dog-to-human bite rate, incubation period, infectious period, probability of human developing rabies following exposure and without treatment, post-exposure prophylaxis coverage, annual number of rabid dogs, vaccination coverage | Cost-effectiveness sensitivity analysis | 90% dog vaccination coverage | Beyene et al., 2019 | ||
| Deterministic compartmental | Zhang, 2011 | NO | Simulation | Rabies dynamics | Vaccination coverage, birth rate | =50% dog vaccination coverage | Taib et al., 2019 | ||
| Deterministic compartmental | NO | Least-square fitting | R | Huang et al., 2019 | |||||
| Stochastic agent-based |
Dürr and Ward, 2015 Hudson et al., 2019 |
YES | Simulation | Explorer, roamer, stay-at-home | Dog vaccination targeting explorer and roamer dogs | Hudson et al., 2019 | |||
| Stochastic agent-based | NO | Simulation | R in the first month | Outbreak duration and size, Re | Dog population size, degree of connectivity, incubation period, clinical periods | 90% dog vaccination coverage | Brookes et al., 2019 | ||
| Stochastic agent-based | Dürr and Ward, 2015 | YES | Simulation | Outbreak duration, number of rabid dogs | Hudson et al., 2019 | ||||
| Stochastic metapopulation | YES | Simulation | Persistence probability, endemic prevalence per patch, R, birth rate | Dog movement bans and massive dog vaccination campaigns in urban areas | Colombi et al., 2020 | ||||
| Note: | |||||||||
| Abbreviations: MCMC, Markov Chain Monte Carlo; R, reproduction ratio; Rc, constrained reproduction number |