Hainan Province is located in the southernmost part of China, with a total land area of 35,400 square kilometers, a sea area of about 2 million square kilometers [18], and a total population of more than 10,081,200 people in the province (mainly including Hainan Island and the Xisha, Zhong Sha, and Nansha Islands). Hainan Province currently has 19 cities and counties, including 4 prefecture-level cities, 5 county-level cities, 4 counties, 6 autonomous counties and 8 districts. Hainan Island has a tropical monsoon maritime climate with distinct wet and dry seasons. The rainy season generally occurs from May to October, and the dry season is from November to April. The province has 62.1% forest cover and is a natural habitat for many types of snakes. Especially in the central part of the city snake is the most, the central part of Hainan Province is surrounded by mountains, and is a big mountain, rainfall is sufficient, the mountain has a longitudinal forest of shrubs, suitable for the survival of snakes, such as Qiong Zhong, Wu Zhi Shan and Bao ting and so on.

Vector data of Hainan Province’s administrative regions are from the standard map production with the review number: Qiong S (2023) 130 downloaded from the standard map service website of Hainan Survey and Mapping Geographic Information Bureau, with no modification of the base map, see Supplementary File 1. Haikou traffic network data from the National Center for Basic Geographic Information (NCBGI) 1:1,000,000 public version of the basic geographic information vector data. Multiple road files are combined and retained in a shapefile format.

The population distribution raster data for 2020 was obtained from the official World Pop website, and finally the World Pop 100 m*100m precision population raster data for 2020, corrected by the seventh census data at the street level, was used. World pop data is the number of people per 100 m² scale grid estimated by the Random Forest method based on census data and multi-source auxiliary data by the Earth Data Research Institute of the University of Southampton, United Kingdom. The data can better reflect the distribution of the population, and therefore has been widely used in many fields such as urban planning and human geography [19]. In this study, in order to further improve the estimation accuracy of the population raster, the errors present in the original population raster data were corrected utilizing street-level 7th Census data. The specific correction method is: using the seventh census data in the number of street population divided by the number of the original grid summary population to get a linear correction factor, and then the original total population of each street will be multiplied by the correction coefficient, so that the total population of each grid in the street range word and the seventh census data are equal to the details, see Supplementary File 2.

A 2 km*2 km resolution grid was created for the study area with a search radius of 40km, and the generated center-of-mass grids were converted to vector data that were perfectly superimposed on the statistical grid for the study, where each grid had an area of 4 square kilometers. Centers of mass were generated for all these grids (squares), and then proximity tables were generated by neighborhood analysis to incorporate demographic and identifying information.

Snake antivenom are obtained by immunization of animals, and the antivenom in question is an immunoglobulin obtained by immunization of “horses”. The location and availability of health facility sites for antivenom were provided by Shanghai Salem Biological Company, and 25 antivenom availability sites were identified by geographic coordinate conversion using Gao De map. The number of beds and health technicians in medical units are obtained from the Health Statistics Yearbook of Hainan Province and the official websites of each hospital.

OD cost matrix analysis is one of the network analysis methods, which is a method to simulate the representation of the real mesh structure using graph theory and operations research theory [20]. A complete network contains 4 basic elements: center, chain, node, and resistance. In the hospital accessibility study, the hospital coordinate point as the center, the road network from the population center of gravity point to the hospital as the chain, the road intersection as the node, and the time spent moving on the road as the resistance, in order to build a visual digital model for the simulation of the real path of the population center of gravity point to reach the hospital.

Based on the network analysis method, this paper uses the target starting point as the shortest distance/time from each population center of mass point, i.e., demand center, directly to the antivenom equipped hospitals to determine the ease of access from the population center of mass point to the hospitals and service utilization. This is done by obtaining the optimal path from the population center of mass point to each antivenom-equipped hospital and the optimal time cost by using the cost matrix between the population center of mass point and the antivenom-equipped hospital and the nearest facility point.

The two-step floating catchment area method (2SFCA) is a method for evaluating accessibility. The method integrates the relationship between the supply of resources and the demand in the vicinity, and is simple and rigorous in its calculations.

In the first step, the first point j is used as the center of the hospital location, and the search radius is established with the limiting distance d o of the road network for people to go to the hospital as the search radius, and all the populations within the search domain j are summarized, and Gaussian functions are used to assign weights according to the law of distance attenuation, and these weighted populations are summed and aggregated to compute the ratio of supply to demand R j : R j = S j ∑ k ∈ d j k ≤ d o G d i j D k (1) where D k is the population number of each population center of mass point k, d_jk is the road network distance between locations k and j. The road network distance from the demand unit to the nearest entrance is selected, and the unit k needs to fall within the search domain (i.e., d j k ≤ d o ); S j is the number of beds/health technicians in hospital j; G d i j is a Gaussian decay function considering the spatial friction problem, which can be expressed in the specific form: G d i j = e − 1 2 × d o d i j 2 − e − 1 2 1 − e − 1 2   d i j < d o (2)

In the second step, with each population center-of-mass point i as the center, search for all the healthcare institutions j within the threshold range ( d o ), and summarize and superimpose the hospital location points to get the ratio of the number of beds/health technicians to the population of the hospitals in the final search domain ( R j ), i.e., we get the accessibility of the number of beds/health technicians in the i points ( A i ), and the larger the value means the higher the degree of accessibility: see Equation 3. A i = ∑ j ∈ d i j ≤ d o G d i j R j (3)

The supply/demand ratios for each supply radius were determined in turn from Equations 1–3, and finally the accessibility of the number of beds/health technicians for the study population was determined.

Threshold setting: Since antivenom provisioning requires cold chain and high requirements for hospitals and healthcare workers, the service radius was set to 40 km for analysis respectively.

Considering the differences in antivenom equipped hospitals and service capacity, hospitals were set to be reached by car, with a 15-minute drive time (40 km road network distance) as their spatial search threshold. According to the average peak hour travel speed of the road traffic operation index system in Hainan Province, the province’s roads are divided into the types of highways, expressways, arterial roads, feeder roads, other, internal, rural, bicycle, and pedestrian roads, and the travel speeds are set to 100, 80, 60, 20, 20, 20, 30, 15, and 5 km/h, respectively. The supply, demand and optimal path time results were substituted into the Gaussian two-step moving search method formula to calculate the accessibility of antivenom-equipped hospitals in Hainan Province and to analyze the number of beds available for 1,000 people and the number of health technicians for 1,000 people, respectively.

As shown in Table 1, the number of population centers of mass to find the destination hospital was 8,707, and the number of population centers of mass that could reach the hospital in less than 30 min totaled 4,055, accounting for 46.6% of the total, covering an area of about 16,220 square kilometers, or about 3,703,700 people; The total number of population centers of mass greater than 30 min and less than or equal to 60 min or less is 4,106, or 47.2%, covering an area of about 16,424 square kilometers and about 4,077,100 people; The total number of population centers of mass greater than 60 min and less than or equal to 90 min or less is 498, or 5.7%, covering an area of about 1,992 square kilometers and about 587,300 people; The total number of population centers of mass greater than 90 min and less than or equal to 120 min or less is 48, or 0.6%, covering an area of about 192 square kilometers and about 38,000 people.

Hyalys antivenom, Naja antivenom, Bungarus multicnctus antivenom, Agkistrodon Acutus antivenom equipped hospital, and equipped with antivenom for all species of snakes in the country.

As can be seen from Table 1, the number of population centers of mass to locate hospitals for Agkistrodon Hyalys snake antivenom was 8,708, and the total number of population centers of mass that could reach the hospitals in less than 30 min was 3,855, which accounted for 44.3% of the population, and covered an area of about 15,420 square kilometers, or about 3,452,500 people; The total number of population centers of mass greater than 30 min and less than or equal to 60 min or less is 4,159, or 47.8%, covering an area of about 16,636 square kilometers and about 4,098,700 people; The total number of population centers of mass greater than 60 min and less than or equal to 90 min or less is 645, or 7.4%, covering an area of about 2,580 square kilometers and about 811,800 people; The total number of population centers of mass greater than 90 min and less than or equal to 120 min or less is 49, or 0.6%, covering an area of about 196 square kilometers and about 44,400 people. See Figure 1 for details.

As can be seen from Table 1, the number of population centers of mass that found hospitals equipped with Naja antivenom was 8,707, and the total number of population centers of mass that could reach the hospitals in less than 3 0 min was 2,118, or 24.3%, covering an area of about 8,472 square kilometers, or about 2,318,400 people; There are a total of 3,971 population centers of mass greater than 30 min and less than or equal to 60 min or less, accounting for 45.6% of the total, covering an area of about 15,884 square kilometers and about 3,775,500 people; There are a total of 2,153 population centers of mass greater than 60 min and less than or equal to 90 min or less, accounting for 24.7% of the total, covering an area of about 8,612 square kilometers and about 2,089,900 people; The total number of population centers of mass greater than 90 min and less than or equal to 120 min or less is 444, or 5.1%, covering an area of about 1,776 square kilometers and about 215,600 people; The total number of population centers of mass greater than 120 min is 21, or 0.2%, covering an area of about 54 square kilometers and about 0.7 million people. See Figure 2 for details.

As can be seen from Table 1, the number of population centers of mass that found hospitals equipped with Bungarus multicnctus antivenom was 8,707, and a total of 1,799 population centers of mass that could reach the hospitals in less than 30 min, accounting for 20.7% of the total, covering an area of about 7,196 square kilometers and about 2,177,600 people; The total number of population centers of mass greater than 30 min and less than or equal to 60 min or less is 3,683, or 42.3%, covering an area of about 14,732 square kilometers and about 3,157,600 people; There are a total of 2,510 population centers of mass greater than 60 min and less than or equal to 90 min or less, accounting for 28.8% of the total, covering an area of about 10,040 square kilometers and about 2,516,900 people; There are 654 population centers of mass greater than 90 min and less than or equal to 120 min or less, accounting for 7.5% of the total, covering an area of about 2,616 square kilometers and about 516,700 people; The total number of population center of mass points greater than 120 min is 61, or 0.7%, covering an area of about 244 square kilometers and about 37,300 people. See Figure 3 for details.

As can be seen from Table 1, the number of population centers of mass to locate hospitals equipped with Agkistrodon Acutus antivenom was 8,707, and a total of 1,695 population centers of mass that could reach the hospitals in less than 3 0 min, accounting for 19.5% of the total, covering an area of about 6,780 square kilometers and about 2,240,900 people; The total number of population centers of mass greater than 30 min and less than or equal to 60 min or less is 4,045, or 46.5%, covering an area of about 16,180 square kilometers and about 3,498,900 people; There are a total of 2,521 population centers of mass greater than 60 min and less than or equal to 90 min or less, accounting for 29.0% of the total, covering an area of about 10,084 square kilometers and about 2,449,900 people; The total number of population centers of mass greater than 90 min and less than or equal to 120 min or less is 415, or 4.8%, covering an area of about 1,660 square kilometers and about 181,300 people; The total number of population centers of mass greater than 120 min is 31, or 0.4%, covering an area of about 124 square kilometers and about 35,200 people. See Figure 4 for details.

As can be seen from Table 1, the number of population centers of mass where hospitals equipped with the antivenom for all species of snakes were found was 8,707, and the total number of population center of gravity where hospitals could be reached in less than 30 min was 805, or 9.3%, covering an area of about 3,220 square kilometers, or about 1,421,700 people; The total number of population centers of mass greater than 30 min and less than or equal to 60 min or less is 2,491, or 28.6%, covering an area of about 9,964 square kilometers and about 2,263,500 people; The total number of population centers of mass greater than 60 min and less than or equal to 90 min or less is 2,898, accounting for 33.3% of the total, covering an area of about 11,592 square kilometers and about 2,782,500 people; The total number of population centers of mass greater than 90 min and less than or equal to 120 min or less is 1,794, or 20.6%, covering an area of about 7,176 square kilometers and about 1,462,000 people; The total number of population centers of mass greater than 120 min is 719, or 8.3%, covering an area of about 2,876 square kilometers and about 476,400 people. See Figure 5 for details.