Optimization of Precontrol Methods and Analysis of a Dynamic Model for Brucellosis: Model Development and Validation

Introduction

Infectious diseases enter the human body through pathogens such as bacteria, fungi, or viruses, causing bodily damage or even death. In serious cases, infectious diseases cause large-scale transmission of diseases among the population [1]. Furthermore, the number of diseases transmitted from animals to humans is increasing at an alarming rate. Viruses mutate over time, and some mutations make them more suited to living in the current environment and the physiological states of various hosts [2]. More than 60% of the infectious diseases in humans are caused by animals and more than half of animal diseases can be transmitted to humans, which underscores the need for researchers to study such diseases [3]. The infectious disease investigated in this study is brucellosis, which is a zoonotic disease caused by Brucella [4].

Brucella is a gram-negative, nonmotile bacterium without a capsule. It is an aerobic intracellular parasite that can reduce nitrates. Brucella has a strong ability to adapt to the environment, which makes it able to tolerate dryness and cold temperatures and survive in meat or dairy products for up to 2 months. However, Brucella is not heat-resistant and is killed by boiling water. Common disinfectants need several hours to destroy Brucella.

In terms of transmission, Brucella passes through the digestive tract, the respiratory tract, the skin, and mucous membranes. By eating Brucella-contaminated food or contacting animals or animal secretions and excretions infected with Brucella, humans can become infected with Brucella [5]. Once infected with Brucella, the infected person will go through the acute and chronic stages of brucellosis. At first, the infected person is in the acute stage, at which time they will have symptoms of other systemic diseases. During this stage, brucellosis is relatively easily cured; however, the infection is often not effectively diagnosed as brucellosis at this point. After the infected person enters the chronic stage, brucellosis is very difficult to cure [6].

At present, most of the studies on the transmission of brucellosis are in single populations. When studying the process of infection, transmission between humans is ignored, and only direct infection is considered. However, the transmission process of brucellosis is complicated, and its transmission form is not the same in different regions and between populations. Due to its asymptomatic characteristics, an outbreak of brucellosis is often synchronized between humans and animals. Investigating the spread of brucellosis would help researchers understand and prevent the onset and large-scale transmission of brucellosis. Researchers have built a model for the transmission of brucellosis between humans and flocks. The effects of different control methods on the transmission of brucellosis are known, which aids researchers in designing more effective methods to inhibit the spread of brucellosis [7]. Other researchers have built a mixed model of brucellosis based on sheep-bovine-human transmission. This transmission model revealed that disinfection and immunization are the two most effective inhibitory measures against the transmission of brucellosis [8]. This study explores the transmission of brucellosis among goats to provide theoretical support for the suppression of brucellosis.

By understanding the effect that control measures have on transmission suppression, we can create theoretical support for the suppression of infectious diseases [9]. The objective of this study was to construct a mathematical model of brucellosis infection. By studying the transmission characteristics of Brucella and building a Brucella transmission model, the precontrol methods for key populations (Brucella-susceptible populations) were designed. We then determined the utilization rate of protective tools by key groups before and after a presentation on precontrol methods. This study provides theoretical support for the suppression of Brucella and protective measures for key populations.

Methods

Proposed Algorithm

Model Construction

Based on the characteristics of Brucella transmission from goat flock to humans, we built a model of Brucella transmission that divides the flock into two groups: ordinary ewes and other goats. In addition, we divided the ordinary female flock further into susceptible goats, infected goats, and vaccinated goats. The human population was divided into two groups: susceptible and infected people. Additionally, infected people were divided into acute and chronic infections. Models were built based on the characteristics of Brucella transmission. The following hypotheses were made: (1) There is no route of infection among humans. Brucella infections in humans come from direct or indirect contact with goats. (2) Goats and humans have natural deaths. (3) The number of human births and the number of goat flocks are considered, as are the natural death of bacteria and bacterial death caused by disinfection. The transmission of brucellosis is shown in Figure 1. The diamonds represent the ordinary ewes, the rounded rectangles represent other goats, and the rectangles represent the human population.

In Figure 1, S_a, V_a, E_a, and I_a represent ordinary ewes that are susceptible, vaccinated, inapparently infected, and isolated positive infections, respectively,. S_b, V_b, E_b, and I_b represent susceptible, vaccinated, inapparently infected, and isolated positive infections of other goats, respectively. W represents Brucella in the environment, while S_c, I_c, and Y_c represent susceptible, acute, and chronic human populations, respectively. As shown in Figure 1, Brucella infection among susceptible human populations can be caused by Brucella in the environment and inapparently infected goats in the flock. Brucella in the environment is caused by the inapparently infected goats and the isolated positively infected goats. Additionally, Brucella dies naturally in the environment. Therefore, the differential equation of Brucella transmission can be obtained, as shown in Equations 1-12.

In these equations, A is the input constant value, b is the probability of each infection, m is the conversion rate of the young to mature goats, d is the production rate, t is the ratio of the adult and young infection rates in the flock, which should be between 0 and 1 combining with the actual situation, a is the mortality rate of infected sheep due to brucellosis, k is the release rate of infected bacteria per unit time, and d is the Brucella mortality rate in the entire goat flock.

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Model Dynamics

Since the last 3 equations are independent of the previous 9, only the first 9 equations are included when considering model dynamics. Within equations 1-9, an equilibrium point free of brucellosis can be found, represented by the equation below:

.

The resulting positive invariant set of the research system is as follows:

Numerical Simulation

Based on the number of brucellosis cases reported on the internet, a hypothetical estimation and numerical simulation process were performed. The values used in the numerical simulation are described here. First, 2-3 years is the inventory time of ordinary ewes, and the number of ewes is about 4.2 million; therefore, the average removal rate of ordinary ewes d_b is 0.4, and the supplement amount of ordinary ewes A_b is 1.68 million. According to the actual data, the production rate of the flock is about 60%. Therefore, the removal rate of other goats is 0.6, and the supplement amount is 1.976 million. Second, according to population data, the natural death rate in the human population is 5.68%; thus, the supplement rate of the human population is estimated, and the supplement amount is about 9,150. Third, according to the existing data, the culling rate of infected goats can reach 0.15; therefore, the positive detection rate of ordinary ewes and other goats was set to 0.15 for this model. Additionally, according to the average 1-month survival time of affected goats, the culling rate of infected ewes and other goats is set to 12.

Precontrol Methods of Brucellosis

Studies have shown that the daily behavior of susceptible populations (that is, those with high frequency of contact with animals) is the key to whether brucellosis can be effectively transmitted, and that the irregular daily behaviors of susceptible populations greatly increase the rate of Brucella infection; thus, it is important for them to protect themselves during daily exposure [10]. Due to the generally low level of education of the key populations in this study, they lack self-protection awareness and knowledge of protective measures to varying degrees. In their daily contact with animals or related products, they cannot achieve comprehensive and universal protection from Brucella infections.

The precontrol methods in this study included giving lectures on prevention, control, and health education to the experimental population, so that they would have a comprehensive understanding of Brucella. This laid the foundation for additional precontrol works. Subsequently, Brucella bacterial preventive tools (such as gloves, masks, and disinfectants) were distributed to the key populations and the relevant preventive training was delivered, followed by a question and answer session that answered the key populations’ questions about Brucella protection. This strengthened their protection awareness and led them to change their daily habits and use of protective tools. The experimental population involved in this study was the staff on a farm. All personnel were included in the experiment and signed informed consent forms.

Follow-up visits or phone calls were made to infected patients to understand whether they are used to the corresponding prevention and control behaviors, and whether their prevention and control behaviors are correct. Additionally, any questions that susceptible populations and infected patients have about brucellosis should be answered promptly to reduce panic and strengthen the effect of precontrol methods.

Statistical Methods

SPSS 22.0 software (IBM) was used to statistically analyze the data obtained in this study and make corresponding statistical descriptions. The Chi-square test was used to statistically analyze the clinical characteristics of the diseased populations with different disease forms and different Brucella contact history. P<.05 indicates that the difference is statistically significant. For comparison between multiple groups, the Chi-square test was used, and the check level was a=2a/k(k-1), where k is the number of grouping groups, and P<a represents that the differences are statistically significant.

Results

Results of the Numerical Simulation

The numerical simulation process was performed according to the actual data, which enabled us to generate the data shown in Figure 2. As shown in Figure 2, the numerical simulation suggested that the number of people with brucellosis will be stable in the future.

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Precontrol Results of Brucellosis

The mathematical model of this study suggests that humans are infected with Brucella through direct or indirect contact with animals. Therefore, to avoid Brucella infection, it is necessary to first isolate humans from Brucella, a process in which utilizing many protective tools is the most critical step.

The distribution of brucellosis in the study population is shown in Figure 3, demonstrating that the majority of brucellosis patients are men, and the difference in gender distribution is statistically significant (P<.001). In addition, most brucellosis patients are aged 30-59 years. One possible reason for this is that the experimental population was the staff of a farm, where most staff are in that age range.

Figure 4 shows the proportion of different symptoms experienced in different stages of the disease. As shown in Figure 4, the clinical manifestations of patients with brucellosis in the acute stage are mostly fever, pain in muscles and joints, sweating, and fatigue. The above clinical phenomena are significantly more common in patients in the acute stage than those in the chronic stage. The difference is statistically significant (P=.006). Conversely, liver and spleen enlargement occurred at both disease stages, and the difference was not statistically significant. However, the probability of testicular enlargement in patients was significantly higher in the acute stage than in the chronic stage; the difference was statistically significant (P=.003). Finally, the likelihood of lymphadenopathy in patients in the chronic stage is significantly higher than that in patients in other stages (P=.005).

Figure 5 shows the utilization of protective tools by the key populations before and after the intervention. As shown in the figure, the utilization of protective tools by the key populations improved significantly following the intervention. Many people in the key populations now wear gloves, masks, rubber shoes, hats, and work clothes; wash their hands frequently; and disinfect animal shelters. The improvement in glove-wearing was the most striking, as it increased from 51.01% before the precontrol methods to 66.22% after the precontrol methods, an increase of 15.21%. The difference was statistically significant (P<.001). However, hat-wearing did not improve significantly (P=.08). It increased from 57.3% before the precontrol methods to 58.6% after the precontrol methods, an increase of just 1.3%.

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Discussion

Overview

Brucella has a strong ability to adapt to the environment. It can tolerate dryness and cold temperatures, and can survive in meat and dairy products for up to 2 months. Presently, it is not possible to completely remove the infection sources of brucellosis. Additionally, it is not currently possible to develop a practical and effective vaccine for brucellosis. Studies have shown that the daily behavior of susceptible populations (that is, those with a high frequency of contact with animals) is the key to whether brucellosis is transmitted further. Indeed, the irregular daily behaviors of susceptible populations could greatly increase the rate of Brucella infection; thus, it is important that they protect themselves when in contact with animals, consistent with previously published research [11] on the suppression of brucellosis transmission.

In this study, we first designed a transmission model of Brucella in animals and humans. It found that human infection by Brucella is through direct or indirect contact with animals. Therefore, to avoid Brucella infection, it is necessary to be isolated from animals infected with Brucella. The utilization of various protective equipment and tools is critical. Prior to the precontrol methods and information dissemination, due to the generally low level of education in the key populations studied, people lacked knowledge about protective measures to varying degrees. When in daily contact with animals or related products, people in these key populations could not achieve comprehensive and universal protection from Brucella infections.

After the precontrol methods in this study, the study populations improved their use of protective tools compared to before the precontrol methods. The utilization of several protective tools improved to varying degrees. In particular, the improvement in glove-wearing was the most striking, as it increased from 51.01% before the precontrol methods to 66.22% after the precontrol methods, an increase of 15.21%. The difference was statistically significant (P<.001). However, hat-wearing did not improve significantly (P=.95), as it increased from 57.3% before the precontrol methods to 58.6% after the precontrol methods, an increase of 1.3%. A possible reason is that people in the key populations do not notice the protective effects of wearing a hat during daily contact with animals; thus, they do not pay attention to wearing hats as protection. The research results also reflected the age distribution and level of education of the key populations; their acceptance of information is slow, and their acceptance of new knowledge is low. However, in general, the utilization of protective tools by the key populations improved significantly. Most people in the key populations wear gloves, masks, rubber shoes, hats, and work clothes; wash their hands frequently; and disinfect animal shelters.

Conclusion

This study researched brucellosis transmission and the effects of precontrol methods on protective equipment usage by key populations. The results of our numerical simulation indicated that the incidence of brucellosis is projected to become stable, without a major increase or decrease. After the precontrol methods, the utilization of protective tools by the key populations improved significantly. Most people in the key populations wear gloves, masks, rubber shoes, hats, and work clothes; wash their hands frequently; and disinfect animal shelters. This study achieved our objectives, but there are still some deficiencies in the research process. Due to the limitation of time, this study failed to analyze the prevalence of brucellosis in key populations after the precontrol methods. In a future study, we aim to research precontrol methods and the subsequent number of brucellosis infections.