The Study Of Human Monkeypox Disease in 2022 Using The Epidemic Models: Herd Immunity And The Basic Reproduction Number Case
Jun 06, 2023
Abstract
As of May 2022, a new outbreak of the human monkeypox (MPOX) disease appeared in multiple countries, where the 2022 human MPOX disease spread to more than 109 cases, excluding the suspected cases up to the end of 2022. The deaths of the 2022 human MPOX exceeded 200 cases up to the same date. The human MPOX is not a new disease, this disease was once endemic in some countries on the African continent. Despite this, this disease began to spread in several countries around the world in 2022. The first case of the 2022 human MPOX was recorded in the United Kingdom in May. After that date, this disease began to become a pandemic in several other countries, such as the United States, Spain, and Brazil.
The 2022 human MPOX is a type of viral disease caused by a viral virus, the MPOX virus, and this virus causes rashes and lesions over the skin of the patient, as well as in the mouth of the patient. Multiple effective indicators are employed for the study of 2022 of the human MPOX, such as the herd immunity of the human MPOX (HIhMPOX), the basic reproduction number of the human MPOX (BRNhMPOX), and the infection period of the human MPOX. This study focuses on the study of herd immunity and the basic reproduction number of the 2022 outbreak of human MPOX in multiple countries around the world.
This study employed the semianalytical method of the Susceptible compartment S, Infectious compartment I, and Recovered compartment R (SIR) pandemic model including the mortality for the study of the herd immunity, and the basic reproduction number of the 2022 human MPOX disease. It is found that the average value of herd immunity for the human MPOX disease in 2022 equals 0.2194, that is, 21.94% for multiple countries, and equals to 35.52% for the United States, and 30.99% for Spain. Also, it is found that the average value of the basic reproduction number of the 2022 human MPOX disease equals 1.2810 for multiple countries. It is concluded from these values that 21.94% of the total susceptible population has to be immunized in an effective way to prevent the spreading of the disease. Also, based on the previous values, it is concluded that the status of the 2022 MPOX disease is spreading as a pandemic.
MPOX virus is a mammalian virus closely related to human immunity. When the human body is infected with the MPOX virus, the human body's immune system will start to respond and produce defense mechanisms such as antibodies to resist the virus.
After infection, the body's immune system usually produces enough antibodies to fight the virus within days and has a long-term immune memory. These conditions can cause the infection to become more severe and persistent if the immune system does not respond adequately to the MPOX virus, or if the immune system is compromised, such as a hyperfunctioning immune system, or if drugs such as chemotherapy or immunosuppressants intervene.
Therefore, maintaining adequate immunity is very important for the prevention and control of the MPOX virus. Good lifestyle habits such as getting enough sleep, eating a nutritious diet, and exercising moderately can help boost your immune system. In addition, vaccination is also an effective way to prevent MPOX virus infection. Therefore, we must pay attention to improving our immunity. Cistanche can significantly improve immunity. Meat ash contains a variety of biologically active ingredients, such as polysaccharides, two mushrooms, and Huang Li, which can stimulate the immune system. Various types of cells, increase their immune activity.
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Keywords:
disease outbreak, epidemic, gay, herd immunity, human monkeypox, models, MPOX, MSM, pox viruses, the basic reproduction number.
Introduction
Human monkeypox (MPOX) is a specific type of viral virus caused by a viral infection called the monkeypox virus. Recently, the human MPOX began to spread over several countries in May 2022. This outbreak of the disease is named the ‘2022 human MPOX disease’. The WHO has relied on naming it the 2022 human MPOX, and we use this term in the study[1]. Multiple studies discussed the 2022 human MPOX status, for example; it is found detection of traces of the MPOX in wastewater with sparse sampling from Asian densely populated areas [2]. Also, some studies discussed applying the epidemic models, including the fractional models, and other control models[3–5]. Other studies discussed the possible vaccinations of the 2022 human MPOX, such as studies[6–9].
Also, some studies discussed some of the indicators of the 2022 human MPOX disease, such as the infection period of the pandemic and other indicators[10,11]. Besides, some studies concern the case of the MPOX in a specific country, such as Pakistan[12]. Also, some studies discussed the case of the disease with pregnancy[13]. Although the WHO Centers for disease control and Prevention state that more than ninety percent of the confirmed cases of the 2022 human MPOX disease were reported in persons who have sex men to men (MSM) such as gays people[1,14], some studies discussed the cases of the 2022 human MPOX disease in women[15]. Some studies discussed the case of the 2022 MPOX disease with HIV disease[16].
Another study discussed the possible risk during the 2022 FIFA (Federation International Football Association) World Cup[17]. Also, a study discussed the detection of traces of the disease in clinical samples[18]. Some studies showed specific reviews about the MPOX disease in 2022 or compared it with other diseases[19,20]. The 2022 outbreak of the human MPOX disease began to spread over 111 countries around the world (including the suspected cases) as of the middle of December 2022. First, the first human case of MPOX in 2022 was reported in the United Kingdom by a traveler returning from Africa on 6 May 2022. After that date, a lot of confirmed cases were reported from multiple countries around the world. For example, in the north American countries, the United States reported its first case of the 2022 human MPOX at 18 May 2022, and the total confirmed cases are 29 643 cases up to 13 December 2022[14,21], and Canada reported its first case of the 2022 human MPOX at 19 May 2022, and the total confirmed cases are 1459 cases up to 7 December 2022[22–25].
In South America; Brazil reported its first case of the 2022 MPOX on 17 June 2022, and up to the middle of December 2022, Brazil was the second country with 10 264 confirmed cases[26]. Also, in South America, Argentine reported its first case on 27 May 2022, and as of 8 December 2022 it reported a total number of 972 confirmed cases of the 2022 MPOX disease[27], and Colombia reported 3880 confirmed cases[28] to the same date. Also, up to the same date, Australia reported 144 total confirmed cases[29] of the 2022 human MPOX disease. In the European countries up to the middle of December 2022, Austria reported 327 total confirmed cases, Bulgaria reported six total confirmed cases, and Hungary reported 80 total confirmed cases[14]. Also, on the European continent, and up to the same date, Belgium reported 790 confirmed cases of the 2022 human MPOX disease[30]. France reported 4110 total confirmed cases of the 2022 human MPOX disease[31]. Italy reported 927 total confirmed cases of the 2022 human MPOX disease[32]. While in the United Kingdom, where the first case of the 2022 outbreak of the human MPOX was reported, there were about 3730 cases (https://www.gov.uk/government/publications/monkeypox-out break-epidemiological-overview) up to the same date. Spain is the country with the highest number of total confirmed cases of the 2022 human MPOX where it reported 7408 total confirmed cases[33]. Although Asia is the biggest continent, it reported the lowest number of total confirmed cases of the 2022 human MPOX disease among all of its countries.
For instance, the United Arab Emirates reported 16 total confirmed cases[34], the People's Republic of China reported one confirmed case[35], and Lebanon reported 24 total confirmed cases[14] of the 2022 human MPOX disease to the same date. The total confirmed number of the 2022 human MPOX disease reached about 92 711 cases, including the suspected cases. Some countries applied multiple procedures for limiting the spreading of the 2022 human MPOX. The use of the epidemic models[36–39] for the study of the 2022 MPOX disease spreading is an important tool because these models include lots of important indicators of the disease. Although lots of the recent studies about the outbreak of the 2022 human MPOX diseases focused on the reporting of cases or possible prevention of the disease[40–48], in this study, the simple SIR (Susceptible compartment S, Infectious compartment I, Recovered compartment R) model with mortality is employed for the discussion of herd immunity and the basic reproduction number of the 2022 human MPOX disease.
The Runge–Kutta simulation techniques[49] are
employed for the fitting of the parameters of the model. This
study focuses on finding the indicators of the 2022 human MPOX
disease for multiple countries with more focus on two countries which are the United States, and Spain. The reason for
choosing these two countries is that the United States has the
highest number of 2022 human MPOX cases in the world, and
Spain has the highest number of 2022 human MPOX cases
among the European countries. In the second section of this article, the method used is explained. In the third section, the
results of the study, in addition to the discussion, are illustrated,
while the conclusion of this study is illustrated in the last section
of the article.
Methods
This section of the article deals with the method that is used for finding the basic reproduction number and the herd immunity of the 2022 human MPOX disease. We begin with the main four equations of the SIR model with mortality or death (Death compartment D), that is, the SIRD model. The first equation of the model describes the rate of the susceptible compartment S(t) concerning time t, and this equation is:
The simple SIR model excluding the mortality is given only by three differential equations without the fourth one, and without the third term on the right side of the second equation of the model; this study, however, takes the mortality into account where we use the four compartments of the model.
The fourth compartment of the SIR model is illustrated in Figure 1 as a schematic graph excluding the mortality compartment and in Figure 2 including the mortality compartment.
The three parameters illustrated in the SIRD model describe the coefficients of each compartment. Based on these three parameters, we can find the basic reproduction number of the 2022 human MPOX disease, which is given as follows:
As we see from Equation 5 and the Equation 6, the determination of the herd immunity and the basic reproduction number of the 2022 human MPOX disease requires the finding of the three parameters of the SIRD model. Where we find these three parameters depends on the seminumerical, or semianalytical method of the model. Where we use the Runge–Kutta simulation for the fitting of the reported total confirmed cases of the 2022 human MPOX disease for each country. From this fitting, we determine the three parameters of the 2022 human MPOX disease. After that, we use Equation 5 to find the basic reproduction number of the 2022 human MPOX disease. At each step of the simulation, we apply the conservation condition of the total four population compartments, which is:
where the derivatives in the last equation are concerning the time.
Figure 3 includes an explanation of the method that we apply for finding the herd immunity of the 2022 human MPOX disease and the basic reproduction number of the human MPOX disease. As we see from this schematic figure, first we set the time step of the simulation procedures, and after that, we put the considered dates of the disease. In the next step, we recorded the total confirmed cases of the 2022 MPOX disease, including the mortality confirmed cases, and then we applied the Runge– Kutta simulation method based on the semianalytical procedure of the model. Where we apply the condition of the total population at each step of the time. After that, we determine the coefficients of recovery and mortality, and then we determine the coefficient of the infection. Finally, based on the three coefficients of the SIRD model, we find the basic reproduction number and the herd immunity of the 2022 MPOX disease based on the two related equations, that is, Equation 5 and Equation 6. The method itself requires the determination of the date of the first confirmed case of the 2022 MPOX disease, as well as the date of the first mortality case of the disease.
Results and discussion
Herein, we illustrate the results of the basic reproduction number and the herd immunity of the 2022 human MPOX disease. We focused on multiple countries for the study, and here we mentioned two countries as examples which are the United States, and Spain because these two countries have the highest reported number of total confirmed cases of the 2022 human MPOX disease over the world and the European continent.
For finding these results, first, we determined the date of the first confirmed case of the 2022 human MPOX disease in the United States, which was on 18 May 2022, while the first confirmed mortality case was reported in Texas on 30 August 2022[14,21], and there were 20 confirmed mortality cases up to the middle of December 2022. We used the previous two dates, 18 May and 30 August as the initial conditions of the method for the United States. Based on the method, it is found that the three coefficients of the model for the United States are as follows: the infectious coefficient is 0.1022 per day, the recovery coefficient is 0.0659 per day, and the mortality coefficient is less than 0.0001 per day. Also, the same procedure was applied to Spain, where the first case of the 2022 human MPOX disease was recorded on the same day as the first case in the United States[14,33], while the first confirmed mortality case in Spain was recorded on 29 July 2022. We took these 2 days as an initial condition of the method for Spain. Based on the method, it is found that the three coefficients of the model for Spain are as follows: the infectious coefficient is 0.0507 per day, the recovery coefficient is 0.0338 per day, and the mortality coefficient is about 0.0001 per day.
Based on these calculations, it is found that the herd immunity of the 2022 MPOX disease for the United States equals 0.3552 and the basic reproduction number of the disease equals 1.5508 for the United States. Also, based on the previous calculations, it is found that the herd immunity of the 2022 MPOX disease for Spain equals 0.3099, and the basic reproduction number of the disease equals 1.4490 for Spain. By applying the same method of fitting the coefficients of the model for multiple countries where we considered one country of each continent, it is found that the average herd immunity of the 2022 human MPOX disease equals 0.2194, and it is found that the average basic reproduction number of the 2022 human MPOX disease equals to about 1.2810. Multiple points can be concluded from these values of the two indicators for the outbreak of MPOX disease in 2022, such as the status of the disease and the average percentage of the total susceptible population that has to be immunized effectively. For instance, we see that the total susceptible populations that have to be immunized effectively are 35.52% in the United States and 30.99% in Spain.
Conclusion
This communication focused on discussing the 2022 human MPOX disease using the epidemiologic models. The simple SIR model, including mortality, was applied for this purpose, and two important indicators were found for the 2022 spreading of the human MPOX disease. The two indicators that were found the herd immunity and the basic reproduction number of the 2022 human MPOX disease. The two indicators of the 2022 human MPOX disease were estimated based on the semianalytical method and the Runge–Kutta simulation for fitting the reported data of the 2022 human MPOX disease.
The study focused on the status of the 2022 human MPOX in two countries: the United States and Spain because one of these two countries has the highest number of total confirmed 2022 human MPOX cases in the world, which is the United States, and the other has the highest number of total confirmed 2022 human MPOX cases over the European countries, which is Spain. Also, the study was generalized to other countries to find the average values over multiple continents around the world. It is found that the basic reproduction number values of the 2022 human MPOX for the United States are 1.5508 and for Spain are 1.4490, while the average value of the 2022 MPOX disease basic reproduction number for multiple countries is about 1.2810. The most important conclusion about this value which affects the population is that the infection of the 2022 human MPOX disease starts to spread, that is, the 2022 human MPOX disease is a pandemic in its 2022 outbreak. This can be compared with the previous problem, which is the 2019 coronavirus disease[19,50–53] where it is seen that the spreading rhythm of the 2022 human MPOX disease is less than that of the 2019 coronavirus disease.
Also, it is found that the values of herd immunity for the 2022 human MPOX disease are 35.52% for the United States and 30.99% for Spain. Based on these values, it is concluded that about 36% of the total susceptible population in the United States, and about 31% of the total susceptible population in Spain have to be immunized in an effective way to prevent the spreading of the disease. Besides, it is found that the average value of herd immunity for multiple countries when the same method is applied is 21.94%, which means that about 22% of the total susceptible population has to be immunized in an effective way to prevent the spreading of the MPOX virus disease in 2022. The method can be expanded for the study of the status of the human MPOX disease in 2022 across multiple other countries.
Ethical approval
Not applicable.
Consent
Not applicable to the study.
Sources of funding
Not applicable.
Authors’ contributions
M.A.-R.: conceptualization, methodology, and derivation of the algorithm, software, visualization, writing, and editing.、
Conflicts of Interest disclosure
The author has no conflict of interest.
Research registration unique identifying number (UIN)
None.
Guarantor
Marwan Al-Raeei.
Availability of data and materials
The author confirms that the data is available for non-commercial use.
Provenance and peer review
Not commissioned, externally peer-reviewed.
Acknowledgments
Not applicable.
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