As described in the statistical analysis plan (Additional file 1: Statistical Analysis Plan) [6, 13,14,15], we adopted a decision tree model to simulate human rabies dynamics in different strategies for rabies control, similar to the WHO rabies modelling consortium study for direct comparisons . We used data collected by the Chinese Center for Disease Control and Prevention (China CDC) in the National Human Rabies Surveillance (NHRS) system and also in some provincial surveillance points, including Shandong (East China), Hunan (Central China), Tianjin (North China), Guangxi (South China), Shaanxi (Northwest China) and Guizhou (Southwest China), to investigate potential regional disparities in diverse areas (Additional file 1: Fig. S1). Our study followed the updated Consolidated Health Economic Evaluation Reporting Standards 2022 (CHEERS 2022) checklist  (Additional file 1: CHEERS 2022 Checklist). All analyses were performed in R (Version 4.0.5).
We considered four primary scenarios (Fig. 1 and Additional file 1: Table S1). (1) status quo: rabies prevention is performed according to the current practice in China without IBCM as usual, i.e., victims bitten by dogs and seek PEP treatment in clinics and paid by themselves, while mass dog vaccination remains low, below 70%; (2) expanding PEP access: we assumed that basic health insurance would cover the cost of PEP treatment to increase the probability of health-seeking, receiving and completing PEP treatment; (3) scaling up mass dog vaccination coverage: we assumed that the number of rabid dogs would decrease as dog vaccination coverage increased to 70%, (especially in rural areas by livestock/veterinary sector), as recommended by the WHO . Two sub-scenarios were included: (3a) increased mass dog vaccination coverage based on the status quo, and (3b) increased mass dog vaccination coverage in addition to expanding PEP access. Last but not least, (4) Use of the IBCM: we evaluated the impact of the IBCM approach, where the health sector and livestock/veterinary sector collaborate for the risk assessment of patients bitten by dogs. Four sub-scenarios were considered: (4a) IBCM with current PEP provision according to the status quo, (4b) IBCM with improved free PEP access only, (4c) IBCM with mass dog vaccination only, and (4d) IBCM with enhanced free PEP and mass dog vaccination. All strategies were assumed to start from 2024.
Decision tree model
The decision tree model (Additional file 1: Fig. S2) was used to obtain health outcomes and direct medical costs by simulating the behaviour of a person seeking medical care after being bitten by a dog, with parameters from published literature, expert consultation, and data from the national human rabies surveillance system. In the tree model, the person might be bitten by a rabid or healthy dog and then decide whether to seek medical care for receiving and completing the PEP treatment. Only those bitten by the rabid dog will die from rabies, and the probability of dying from rabies could be reduced by PEP treatment.
The cost-effectiveness analysis was done from the perspective of the policymaker. We measured health outcomes by human rabies deaths, disability-adjusted life-years (DALYs), and calculated costs by direct medical expenses only. The incremental cost-effectiveness ratio (ICER) was reported in terms of cost per death prevented, converting all prices to US dollars in 2020. Based on China’s per-capita gross domestic product (GDP) of 10,410 US dollars in 2020, if the ICER is less than three times per-capita GDP, the strategy is considered “cost-effective”. All scenarios were simulated with a discount rate of 3%, and the time horizon was set from 2024 to 2035.
Model parameters and assumptions
The parameters were divided into three groups based on their role in being bitten by dogs, seeking medical care, and the resulting health outcomes for patients. These categories include parameters related to rabies exposure, healthcare activities, and DALYs and costs. Parameters related to rabies exposure were used to determine the number of people bitten by rabid or healthy dogs. Those related to health care activities were used to calculate the number of human deaths due to dog-borne rabies and medical services used. The parameters related to DALYs and costs were used to calculate the DALYs and estimate the unit cost (i.e., the price weight). The parameter values (including the probability distributions of each probability function) are presented in Additional file 1: Table S2-S4 [6, 9, 16,17,18,19,20,21,22,23,24,25,26,27,28].
Parameters related to the rabies exposure
The probabilities and numbers bitten by dogs were calculated as follows:
$$P_bitten;by;rabid;dog=fracn_dog;in;2020times P_rabidtimes P_biten_man;in;2020$$
$$P_bitten;by;healthy;dog=fracn_bitten;by;all;dog;in;2020-n_dog;in;2020times P_rabidtimes P_rabid;dogn_man;in;2020$$
In the above formulas, (n_man) represents the number of human population. The number in 2020 was obtained from the National Bureau of Statistics of China . The number of dog population, represented by (n_dog), was estimated based on the human population and a constant human-to-dog ratio of 14. It was assumed that the ratio of humans to dogs remained constant over time. The human-to-dog ratio was calculated by dividing the total human population in 2020 (1,412 million) by the number of dogs in the same year (100 million) . We assumed a stable human birth rate (0.852%) and mortality rate (0.707%) to simulate the number of human population from 2021 to 2035. The parameter (n_bitten by all dog) (7.78 million) represents the number of human population bitten by all dogs, was obtained from first-visit cases in rabies PEP clinics from the NHRS system . The rabies incidence in dogs ((P_dog)=0.0003) was estimated by expert consultation based on data from the first Chinese Rabies Surveillance Plan in animal populations during 2004–2018 . Because the average number of bites per rabid dog ((P_bite)=0.38) is currently unavailable in China, we used the same value as the WHO Rabies Modelling Consortium study , for international comparison.
The parameter (P_bitten by rabid dog) represents the probability of a patient being bitten by a rabid dog. It was calculated using Formula (1) by dividing the total human population in 2020 by the number of people bitten by rabid dogs that year. The number of rabid dogs in 2020 was obtained by multiplying the dog population by the rabid incidence in dogs. The number of people bitten by rabid dogs was estimated by multiplying the number of rabid dogs by the average number of bites per rabid dog. We assumed that the probability of being bitten by a rabid dog would remain constant over time and was used to estimate the number of people bitten by rabid dogs beyond 2020 (Formula 3).
The probability of a patient being bitten by healthy dogs is represented by the parameter (P_bitten by healthy dog). We assumed that this probability would remain constant over time and was used to estimate the number of patients bitten by healthy dogs beyond the year 2020 (Formula 4). This value was calculated by dividing the human population in 2020 by the number of patients bitten by healthy dogs that year, as per Formula (2). The number of patients bitten by healthy dogs in 2020 was determined by subtracting the number of patients bitten by rabid dogs from the total number of patients bitten by all dogs ((n_bitten by all dog)).
Parameters related to the health care activities
Human deaths caused by dog-mediated rabies were calculated as follows:
$$n_deaths=P_infecttimes (n_bitten;by;rabid;dog-n_bitten;by;rabid;dogtimes P_seektimes P_receive1times P_completetimes left(P_completetimes left(1-P_receive2right)+P_rigtimes P_receive2right)-n_bitten;by;rabid;dogtimes P_seektimes P_receive1times left(1-P_completeright)times P_prevent)$$
We used the probabilities of seeking medical care ((P_seek)=0.85), receiving PEP treatment ((P_receive1)=0.99), receiving rabies immunoglobulin (RIG) ((P_receive2)=0.17), and completing the PEP regimen ((P_complete)=0.91) from the NHRS system 21, to describe the behaviours of health care activities for patients bitten by a dog. We assumed that (P_seek), (P_receive1) and (P_complete) would change with the improvement of PEP access by a 0.01 increment per year to a cap of 0.9, 0.99 and 0.975, respectively. Consistent with the WHO Rabies Modelling Consortium study , the (P_receive1) would drop by 50% and 90% with IBCM before and after the rabies elimination, respectively. For patients bitten by rabid dogs, the following parameters were used to calculate the probabilities of dying from rabies: the probability of developing rabies without any intervention ((P_infect)=0.16), the probability of avoiding rabies given a complete PEP ((P_prevent)=1), the probability of avoiding rabies given an incomplete PEP ((P_prevent)=0.99) , and the probability of avoiding rabies given an RIG injection ((P_prevent)=1).
Parameters related to DALYs and costs
Consistent with the WHO Rabies Modelling Consortium study , we estimated the mean DALY caused by rabies using data on the age distribution of the human rabies deaths and age-specific life expectancy. Age distribution of the human rabies deaths during 2011–2021 was taken from the NHRS system. The life expectancy in 2024 was estimated by a life table (Additional file 1: Table S5), obtained from the United Nations World Population Prospects 2022 . According to the standard PEP treatment procedure, we only considered the direct costs: registration fee of the first visit, injection fee, costs of wound cleaning, human rabies vaccines, RIG, and dog vaccines (Additional file 1: Table S2). All costs were converted to US dollars at the exchange rate in 2020 (6.8996 Chinese Yuan per 1 US dollar), with a discount rate of 3%.
We performed probabilistic sensitivity analyses (PSA) to examine the robustness of our results. By drawing 1,000 sets of model parameter values from their distributions, we constructed the results’ 95% uncertainty interval (UI). We also separately considered the uncertainty of the following parameters: (1) incidence of rabid dog bites per person annually (the rabid bite incidence); (2) incidence of non-rabid dog bites per person annually (the non-rabid bite incidence); (3) probability of developing rabies with exposure (Pinfect); and (4) probability of preventing rabies by complete or incomplete PEP treatment (Pprevent) in the one-way sensitivity analyses.