A Fuzzy Logic Inference Model for the Evaluation of the Effect of Extrinsic Factors on the Transmission of Infectious Diseases

Abstract

COVID-19 is a contagious disease that poses a serious risk to public health worldwide. To reduce its spread, people need to adopt preventive behaviours such as wearing masks, maintaining physical distance, and isolating themselves if they are infected. However, the effectiveness of these measures may depend on various factors that differ across countries. This paper investigates how some factors, namely outsiders’ effect, life expectancy, population density, smoker percentage, and temperature, influence the transmission and death rate of COVID-19 in ninety-five top-affected countries. We collect and analyse the data of COVID-19 cases and deaths using statistical tests. We also use fuzzy logic to model the chances of COVID-19 based on the results of the statistical tests. Unlike the conventional uniform weighting of the rule base in fuzzy logic, we propose a novel method to calculate the weights of the rule base according to the significance of the factors. This study aims to provide a comprehensive and comparative analysis of the factors of COVID-19 transmission and death rates among different countries.

1. Introduction

Infectious agents such as COVID-19 are a major threat to global health and security, especially in the context of increasing population mobility, urbanisation, and climate change [1]. However, the transmission and mortality of infectious agents are not uniform across different countries or regions, as they depend on various factors that affect the susceptibility, exposure, and response of human populations and pathogens [2]. Understanding these factors and their interactions can help design effective prevention and control strategies and estimate the infection risk based on a fuzzy logic model [3].

Some of the factors that may influence the transmission and mortality of infectious agents are temperature, population density, life expectancy, smoking index, and outsiders’ effect. Temperature can affect the survival and replication of pathogens, as well as the behaviour and immunity of hosts [2]. Population density can reflect the frequency and intensity of contact among individuals, which can facilitate or hinder the spread of infectious agents [1]. Life expectancy can indicate the overall health status and quality of life of a population, which can affect their vulnerability and resilience to infectious agents [4]. The smoking index can measure the prevalence and intensity of tobacco use among a population, which can impair the respiratory and immune systems and increase the risk of chronic diseases that may complicate the infection [5]. Outsiders’ effect can measure the exposure to foreign visitors or products that may introduce or disseminate pathogens [1].

Previous studies have explored some of these factors individually or in relation to specific regions or illnesses. For example, Liu et al. [6] talked about how COVID-19 spreads differently depending on the season. They found that the virus spreads more in colder weather. Lian et al. [7] talked about a surprising increase in COVID-19 cases in the summer of 2022, saying it happened because of really hot weather. They found that almost 70% of those cases might not have happened if there were not heat waves. Several studies [8,9,10,11] analysed the correlation between temperature and infection rate for COVID-19. Kjerulff et al. [12] examined the association of smoking with the risk of infections in a large cohort of healthy blood donors. Few other studies [13,14] found a positive association between the smoking index and the infection rate or death rate for COVID-19. Hamidi et al. [15] found no significant effect of population density on disease transmission or death rates in 913 cities in the USA. Trias-Llimós & Bilal [4] showed that the COVID-19 pandemic severely impacted life expectancy in Madrid, the most affected region in Spain. In another article, Trias-Llimós et al. [16] estimated the impact of the first wave of the COVID-19 pandemic by estimating both weekly and annual life expectancies in Spain and its 17 regions. Cevik et al. [17] analysed the role of age and comorbidities in COVID-19 death rate. Few other studies on COVID-19 can be found in [18,19,20]. However, none of these studies considered all the factors we suggest in this paper or applied a fuzzy logic model with weights derived from statistical tests.

Fuzzy logic models can provide a flexible and intuitive way to model and analyse the factors of infectious agent transmission by incorporating linguistic variables, fuzzy sets, fuzzy rules, and fuzzy inference systems [3]. Fuzzy logic models can handle the vagueness and imprecision of these factors and the non-linearity and uncertainty of their relationships by using fuzzy membership functions, fuzzy operators, and fuzzy reasoning [3]. Fuzzy logic models can also incorporate expert knowledge or empirical data to assign different weights or values to the input parameters or output variables and adjust or optimise the model performance [3]. Several studies applied fuzzy logic models to diagnose or predict infectious agents based on various factors or parameters. For example, Dhiman & Sharma [21] introduced a fuzzy logic technique to assess the risk of COVID-19 based on six parameters such as breathing difficulty, atmospheric temperature, body temperature, etc. Şimşek & Yangın [22] created a fuzzy logic system to swiftly detect COVID-19 risks, using three subsystems for common and rare symptoms and personal information. Shatnawi et al. [23] proposed a smart fuzzy inference system to diagnose COVID-19 based on the symptoms that appear in the patient. A few more related topics are referred to in [24,25,26,27,28,29,30,31].

In this paper, we aim to fill this gap by conducting a comprehensive analysis of the factors that influence the transmission and death rates of COVID-19 across 95 top-affected countries. We collect data from multiple sources and perform statistical tests to validate our assumptions. We then calculate the weights of the input parameters for the fuzzy logic model based on the results of the statistical tests. Based on these weights and input parameters, we design a fuzzy inference system (FIS) that can estimate the chance of transmitting COVID-19 in a region/state.

Motivation: This study is motivated by the need to understand the factors that affect the spread and severity of infectious agents, especially COVID-19, which pose a serious threat to global health and security. By applying a fuzzy logic model with weights based on statistical tests, we aim to provide a flexible and intuitive way to analyse the factors of infectious disease transmission and to estimate the infection risk in different settings. This can help design effective prevention and control strategies and contribute to the existing knowledge in the field.

Objective: The objective of this study is to develop and apply a fuzzy logic model that can estimate the transmission and death rates of COVID-19 based on five factors: temperature, population density, life expectancy, smoking index, and outsiders’ effect. The model is intended to be generalisable to any country or region, using data from 95 top-affected countries as a sample.

The expected results of this study are

• A fuzzy logic model that can estimate the transmission and death rates of COVID-19 based on five factors: temperature, population density, life expectancy, smoking index, and outsiders’ effect.
• A fuzzy inference system (FIS) that can apply the fuzzy logic model to any country or region, using data from 95 top-affected countries as a sample.
• An analysis of the significance and limitations of the fuzzy logic model and the FIS.

This study will help the health authorities to vanish or control the disease by

• Providing a flexible and intuitive way to model and analyse the factors of infectious disease transmission and to estimate the infection risk in different settings.
• Identifying the most influential factors and their interactions that affect the spread and severity of COVID-19.
• Suggesting effective prevention and control strategies based on the estimated transmission and death rates and the implications of the fuzzy logic model.

The rest of the paper is organised as follows. Section 2 describes Data Collection, Processing, and Analysis. Section 3 explains the calculation of input weights for the fuzzy logic model. Section 4 presents the design and implementation of the FIS. Section 5 discourses the results and findings. Section 6 analyses the results. Section 7 concludes the paper and suggests future work.

2. Data Collection, Processing, and Analysis

2.1. Data Collection

We assume that visitor/export–import data, temperature, population density, smoking, and life expectancy are a few factors that may affect the transmission of the disease and also the death rate due to COVID-19. We collected the mentioned data of the top 95 countries as per the numbers of affected cases from https://www.worldometers.info, https://en.wikipedia.org/wiki/Prevalence_of_tobacco_use, and https://www.timeanddate.com/weather/?sort=1&low=c, accessed on 2 July 2020. The collected data are shown in Appendix A.

2.2. Data Processing and Analysis

In this section, we aim to examine the factors that affect the transmission and death rates of COVID-19 across 95 top-affected countries. We used life expectancy, smoking level, population density, and outsiders’ effect (tourism and global export indicators) as the independent variables and total cases, total cases per million, death rate, and death rate per million as the dependent variables. We used t-tests to compare the means of the dependent variables between two groups of countries based on the median values of the independent variables. We also used fuzzy logic to model the chance of transmitting COVID-19 based on the weights of the independent variables derived from the statistical results.

2.2.1. Data Processing

We collected the data from various sources, such as the World Health Organisation, the World Bank, and the United Nations. The data were collected as of 30 June 2020. We cleaned the data by removing any missing, duplicate, or erroneous values. We also checked the data for outliers and normality. We sorted the data according to the independent variables in ascending order. We then divided the data into two groups based on the median values of the independent variables. For example, for life expectancy, we divided the data into a low life expectancy group (less than or equal to 76.65 years) and a high life expectancy group (greater than 76.65 years). We performed the same for smoking level, population density, and outsiders’ effect.

2.2.2. Data Analysis

We performed t-tests to test the null hypothesis that there are no significant differences in the means of the dependent variables between the two groups of countries for each independent variable. We used a significance level of 0.05. We reported the mean, variance, observations, pooled variance, degrees of freedom, t-statistic, p-value (one-tail and two-tail), and t-critical value (one-tail and two-tail) for each t-test. We also presented the results in tables for each independent variable. We rejected the null hypotheses if the p-value (two-tail) was less than 0.05 and accepted them otherwise.

We found that life expectancy and outsiders’ effect had significant effects on the death rate and the total cases of COVID-19, respectively. We also found that smoking level, population density, and temperature had no significant effects on any of the dependent variables. We concluded that life expectancy and outsiders’ effect were the most important factors for the transmission and mortality of COVID-19, while smoking level, population density, and temperature were less relevant.

We also used fuzzy logic to create a model that can estimate the chance of transmitting COVID-19 in a region/state based on the four independent variables. We used the following steps to create the model:

Step 1: We selected the independent variables that had significant effects on the dependent variables based on the t-tests. We chose life expectancy and outsiders’ effect as the input variables for the fuzzy logic model.

Step 2: We calculated the weights of the input variables based on the p-values of the t-tests. We used the following formula: Weight percentage = (1 − p-value) * 100/2.15788, where 2.15788 is the sum of the 1 − p-values of all the independent variables. We rounded the weight percentages to the nearest integer. We obtained the following weights: outsiders’ effect: 46%, life expectancy: 21%, temperature: 10%, and others: 23%.

Step 3: We defined the fuzzy sets and the membership functions for the input and output variables. We used three fuzzy sets for each variable: low, medium, and high. We used triangular membership functions for the input variables and trapezoidal membership functions for the output variable. We used the median values of the input variables to define the breakpoints of the membership functions. We used the following ranges for the output variable: low: [10, 12.5], medium: (12.5, 16.5), and high: [16.5, 20].

Step 4: We defined the fuzzy rules for the inference process by a specific fuzzy rule base.

Step 5: We applied the fuzzy inference system to the input data and obtained the output values. We used the Mamdani method for the inference process and the centroid method for the defuzzification process. We presented the output values in graphs and tables.

Case 1 (Life expectancy): Life expectancy is a statistical indicator of how long an individual is predicted to live on average based on their birth year, current age, and other demographic variables such as biological sex. It is different in different regions and periods. The death rate due to COVID-19 is higher in countries where life expectancy is higher. In this section, the analysis is performed.

H₀-Null Hypothesis. 

There are no significant differences in death rate when comparing low (less than or equal to 76.65 years) to high values (greater than 76.65 years) of life expectancy of COVID-19-affected countries.

H₁-Alternative Hypothesis. 

There are significant differences in death rate when comparing low (less than or equal to 76.65 years) to high values (greater than 76.65 years) of life expectancy in COVID-19-affected countries.

First, data from the countries were sorted as per life expectancy in increasing order. Then, we divided the list into two groups: a country list whose life expectancy is low, less than or equal to 76.65 years, and a list whose life expectancy is high, greater than 76.65 years. Then, we compared the death rates between the two groups. As per the results of the t-test for equal variances, the mean was 0.023584419 for low values and 0.050352366 for high values of life expectancy, and variances are shown in

Table 1. Significant differences in death rate.

	Death Rate of Low Life Expectancy Countries	Death Rate of High Life Expectancy Countries
Mean	0.023584419	0.050352366
Variance	0.000448951	0.001959616
Observations	48	47
Pooled Variance	0.001196161
Hypothesised Mean Difference	0
Degrees of Freedom	93
t Stat	−3.771620183
p$(\mathrm{T} \le$t) one-tail	0.000142487
t Critical one-tail	1.661403674
p$(\mathrm{T} \le$ t) two-tail	0.000284975
t Critical two-tail	1.985801814

[While comparing low (less than or equal to 76.65 years) to high values (greater than 76.65 years) of life expectancy].

. The p-value (two tails) was 0.000284975, which was less than 0.05. Thus, the null hypothesis can not be accepted. Hence, there are significant differences in death rate when comparing low to high values of life expectancy of COVID-19-affected countries. This concludes that life expectancy has a high impact on death chances. Older persons having COVID-19 have death chances almost double those compared to younger people.

Case 2 (Smoking):

H₀-Null Hypothesis. 

There are no significant differences in death rate while comparing low (less than or equal to 0.226 indexes) to high values (greater than 0.226 indexes) of smoking levels of COVID-19-affected countries.

H₁-Alternative Hypothesis. 

There are significant differences in death rate while comparing low (less than or equal to 0.226 indexes) to high values (greater than 0.226 indexes) of smoking levels of COVID-19-affected countries.

Data were sorted as per smoking levels in increasing order. Then, we divided the list into two groups: a country list whose smoking level was low (less than or equal to 0.226 indexes) and a list whose smoking level was high (greater than 0.226 indexes). Then, we compared the two groups. As per the results of the t-test for equal variances, the mean was 0.031749961 for low values and 0.042013 for high values of smoking level, and variances are shown in

Table 2. Differences in death rate.

	Death Rates of Low-Smoking-Index Countries	Death Rate of High-Smoking-Index Countries
Mean	0.031749961	0.042013
Variance	0.000926522	0.001787
Observations	48	47
Pooled Variance	0.001352228
Hypothesised Mean Difference	0
Degrees of Freedom	93
t Stat	−1.360074066
p(T ≤ t) one-tail	0.088547179
t Critical one-tail	1.661403674
p(T ≤ t) two-tail	0.177094358
t Critical two-tail	1.985801814

[While comparing low (less than or equal to 0.226 indexes) to high values (greater than 0.226 indexes) of smoking levels in countries].

. The p-value (two tails) was 0.177094358, which was higher than 0.05. Thus, the null hypothesis is accepted. Hence, there are no significant differences in death rates when comparing low (less than or equal to 0.226 indexes) to high values (greater than 0.226 indexes) of smoking levels in COVID-19-affected countries. This concludes that the smoking level of a person has a minor impact on death. Highly smoking persons having COVID-19 have death chances larger (but not significantly) compared to non-smoking people.

Case 3 (Population density):

H₀-Null Hypothesis. 

There are no significant differences in affected cases (affected cases/million) while comparing low (less than or equal to 92/sqkm) to high values (higher than 92/sqkm) of population density of COVID-19-affected countries.

H₁-Alternative Hypothesis. 

There are significant differences in affected cases (affected cases/million) while comparing low (less than or equal to 92/sqkm) to high values (higher than 92/sqkm) of population density of COVID-19-affected countries.

Data were sorted as per population density in increasing order. Then, we divided the list into two groups: a country list whose population density was low (less than or equal to 92/sqkm) and a list whose population density was high (higher than 92/sqkm). Then, we separately compared the two groups for affected cases and affected cases/million. In

Table 3. Differences in affected cases of COVID-19 due to population density.

	Affected Cases in Low Density	Affected Cases in High Density
Mean	157,615.1458	67,599.87234
Variance	$2.03787\times 10^{11}$	11,693,419,305
Observations	48	47
Pooled Variance	$1.08773\times 10^{11}$
Hypothesised Mean Difference	0
Degrees of Freedom	93
t Stat	1.330035917
p(T ≤ t) one-tail	0.093379558
t Critical one-tail	1.661403674
p(T ≤ t) two-tail	0.186759117
t Critical two-tail	1.985801814

, the results of affected cases are shown, and in

Table 4. Population density (low and high).

	Total Cases/1 M in Low Density	Total Cases/1 M in High Density
Mean	3595.5	3507.297872
Variance	16,493,772.38	36,211,163.34
Observations	48	47
Pooled Variance	26,246,460.39
Hypothesised Mean Difference	0
Degrees of Freedom	93
t Stat	0.083897967
p(T ≤ t) one-tail	0.466658944
t Critical one-tail	1.661403674
p(T ≤ t) two-tail	0.933317888
t Critical two-tail	1.985801814

, affected cases/million are shown. p-value (two tails) was 0.186759117 for Table 3 and 0.933317888 for Table 4; these were large values (greater than 0.05). Thus, the null hypothesis is accepted for both cases. Hence, there are no significant differences in affected cases while comparing low to high values of population density of COVID-19-affected countries. This concludes that the population density of a country has no impact on COVID-19 transmissions.

Case 4 (Outsiders’ effect):

H₀-Null Hypothesis. 

There are no significant differences in affected cases (or affected cases/million) while comparing low (less than or equal to 0.2 global sharing) to high values (greater than 0.2 global sharing) of percentages of outsiders (tourism and global export indicators) of COVID-19-affected countries.

H₁-Alternative Hypothesis. 

There are significant differences in affected cases (or affected cases/million) while comparing low (less than or equal to 0.2 global sharing) to high values (greater than 0.2 global sharing) of percentages of outsiders (tourism and global export indicators) of COVID-19-affected countries.

Data were sorted as per sharing percentages of outsiders (tourism/global export indicators) in increasing order. Then, we divided the list into two groups: a country list whose sharing percentages of outsiders (tourism/global export indicators) was low (less than or equal to 0.2 sharing) and a list whose sharing percentages of outsiders (tourism/global export indicators) was high (greater than 0.2 sharing). Then, we compared the two groups for affected cases and affected cases/million separately. In

Table 5. Tourists/export–import indicators.

	Affected Cases in Low Outsiders’ Effect	Affected Cases in High Outsiders’ Effect
Mean	31,275.59	200,222.11
Variance	2,965,654,152	$2.10861\times 10^{11}$
Observations	49	46
Pooled Variance	$1.0356\times 10^{11}$
Hypothesised Mean Difference	0
Degrees of Freedom	93
t Stat	−2.557220227
p(T ≤ t) one-tail	0.006084732
t Critical one-tail	1.661403674
p(T ≤ t) two-tail	0.012169463
t Critical two-tail	1.985801814

, the results of affected cases are shown, and in

Table 6. Tourists/export–import indicators have no significant differences in affected cases/million.

	Total Cases/1 M for Low Indicators Value	Total Cases/1 M for High Indicators Value
Mean	2965.86	4176.09
Variance	17,914,825.92	34,365,400.48
Observations	49	46
Pooled Variance	25,874,781.35
Hypothesised Mean Difference	0
Degrees of Freedom	93
t Stat	−1.158896514
p(T ≤ t) one-tail	0.124732725
t Critical one-tail	1.661403674
p(T ≤ t) two-tail	0.249465449
t Critical two-tail	1.985801814

, affected cases/million are shown. p-value (two tails) was 0.012169463 for Table 5, which was less than 0.05, and was 0.249465449 (greater than 0.05) for Table 6. Thus, the null hypothesis is not accepted for Table 5 and accepted for Table 6. Hence, there are significant differences in affected cases while comparing low to high values of sharing percentages of outsiders (tourism/global export indicators) of COVID-19-affected countries. This concludes that sharing percentages of outsiders (tourism/global export indicators) of a country has a significant impact on the transmission of COVID-19.

Other cases:

A few other cases were also analysed in this section. In

Table 7. Differences in affected cases of COVID-19 due to life expectancy.

	Affected Cases of Low Life Expectancy	Affected Cases of High Life Expectancy
Mean	92,724.85	133,870.81
Variance	57,743,028,575	$1.64221\times 10^{11}$
Observations	48	47
Pooled Variance	$1.1041\times 10^{11}$
Hypothesised Mean Difference	0
Degrees of Freedom	93
t Stat	−0.603435983
p(T ≤ t) one-tail	0.273843824
t Critical one-tail	1.661403674
p(T ≤ t) two-tail	0.547687647
t Critical two-tail	1.985801814

, it is observed that life expectancy has no significant effect on transmission of COVID-19 as the p-value is higher than the 0.05 significance level. In

Table 8. Differences in affected cases of COVID-19 due to temperature.

	Effected Cases for Low Temperature	Effected Cases for High Temperature
Mean	103,716.69	122,645.11
Variance	54,089,839,644	$1.68643\times 10^{11}$
Observations	48	47
Pooled Variance	$1.10751\times 10^{11}$
Hypothesised Mean Difference	0
Degrees of Freedom	93
t Stat	−0.277171863
p(T ≤ t) one-tail	0.391131648
t Critical one-tail	1.661403674
p(T ≤ t) two-tail	0.782263295
t Critical two-tail	1.985801814

, we find that temperature is also a non-significant factor for the transfer of COVID-19.

Table 9. Differences in affected cases of COVID-19 due to smoking.

	Affected Cases in Low-Smoking Countries	Affected Cases in High-Smoking Countries
Mean	157,971.35	67,236.09
Variance	$2.02246\times 10^{11}$	13,200,648,298
Observations	48	47
Pooled Variance	$1.0874\times 10^{11}$
Hypothesised Mean Difference	0
Degrees of Freedom	93
t Stat	1.340879173
p(T ≤ t) one-tail	0.091612808
t Critical one-tail	1.661403674
p(T ≤ t) two-tail	0.183225616
t Critical two-tail	1.985801814

shows that the smoking level of countries has some impact on the transmission of COVID-19. However, these factors are not significant to spread such a deadly disease.

3. Creating Input Weights for Fuzzy Logic Based on Statistical Results and Fuzzy Inference System (FIS)

To define fuzzy logic [32], input variables are to be selected first. In this study, the variables, whose impact of spreading COVID-19 were recorded as per our statistical analysis, are to be considered. To find the weight percentages, we followed the steps below.

Step 1: Check the mean ratio of the two considered groups (low and high) for each factor. If the mean of the first group (lower values) is greater than or equal to the mean of the second group (higher values), that variable will not be considered. Otherwise, go to step 2. For example, the mean of the first group is higher than the mean of the second group in Table 3. Hence, the variable population density is not considered here.

Step 2: The p-values (two tails) of t-test for each selected variable are taken, and the ‘$1-p \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{s}\mathrm{\text{'}}$ are recorded. These values are put in

Table 10. Weight percentages.

Influencing Factors	1 − p-Value	Weight Percentages
Outsiders’ effect	0.987831	46
Life expectancy index	0.452312	21
Temperature	0.217737	10
Others	0.5	23

. For example, the p-values (two tails) of outsiders’ effect (tourism/global export indicators) are considered from Table 5. It is tabulated as outsiders’ effect in Table 10. Similarly, the values of other variables are tabulated in Table 10.

Step 3: It is almost well known that a few factors of the spreading of COVID-19 are still unknown. In our proposed model, we take a variable named ‘others’, and its taken p-value as 0.5 for the default case. Then, all the values of the second column of Table 10 are added, and the sum is 2.15788.

Step 4: The final weight percentage is obtained as follows. $\mathrm{W}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t} \mathrm{p}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{g}\mathrm{e}=\left(1-p \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\right) \ast 100/2.15788$. Based on this formula, the nearest integer values are taken. To simplify the process, we take weight ratio as the outsiders’ effect/life expectancy index/temperature/others = 5:2:1:2.

4. Fuzzy Inference System (FIS) to Find the Chance of Transmission of Some Infectious Agents in a Region/State

Fuzzy inference system [33] grips the imprecise and vagueness data. Fuzzy logic has been used in many areas like automatic control, banks, hospitals, and academic institutions.

The factors associated with affectedness of COVID-19 are taken as outsiders’ effect/life expectancy index/temperature/others = 5:2:1:2. It is implemented in

Table 11. The rule base weights.

	Outsiders’ Index	Life Expectancy	Temperature	Others	Chances of Transmission
low	5	2	1	2	[10,12.5]
medium	7.5	3	1.5	3	(12.5, 16.5)
high	10	4	2	4	[16.5,20]

. To combine these factors, the fuzzy logic inference system is perfect to represent as the factors are imprecise. Hence, to find the chance of affectedness of COVID-19, an FIS is modelled here (see Appendix A for details).

5. Results Analysis

This study concludes that the death rate significantly increases in countries with a life expectancy higher than 77 years of age.

This study also highlights that population density has no major impact either on transmission or death rate increase in countries globally.

Another important result of this study is to capture the outsiders’ impact on the transmission of COVID-19. The data were captured based on the export-sharing index globally and the amount of tourism. We have a significant result that the country whose global export-sharing index is more than or equal to 0.3 has significant chances of disease transmission.

The proposed FIS concludes with a satisfactory result. Two instances are given here. In Figure 1, the input values are 0.1, 0.1, 0.8, and 0.5. The output value is 0.153, which indicates the low chances of transmission. Again, in Figure 2, it is found that if the input values are 0.9, 0.8, 0.8, and 0.5, the output value is 0.847. Thus, based on four input parameters, the chances of transmission can be found.

Figure 1 shows that low outsiders’ effect, low life expectancy, and high temperature are kept, and other parameters are kept neutral. It indicates low chances of transmission. Also, in Figure 2, outsiders’ effect is set high along with life expectancy. But, the result is different. It indicates a high chance of transmission. Thus, life expectancy and outsiders’ effect play a significant role in transmission of infectious disease. In Figure 3 and Figure 4, 3D images are shown corresponding to Figure 1 and Figure 2, respectively. In the 3D images, the X and Y axes are represented as ‘lifeExpectancy’ and ‘outsiders’ effect. The other combinations can be similarly found.

6. Discussion

In this paper, we investigated the factors that influence the transmission and death rates of COVID-19 across 95 top-affected countries. We used a fuzzy logic model to estimate the chance of transmitting COVID-19 in a region/state based on four input parameters: outsiders’ effect, life expectancy, temperature, and others. We also performed statistical tests to validate our assumptions and to calculate the weights of the input parameters for the fuzzy logic model.

Our results show that the death rate significantly increases for countries with a life expectancy higher than 77 years of age. This is consistent with previous studies that have found that older age groups and males are more vulnerable to COVID-19 and have higher mortality rates [4,17,34,35]. This may be due to the higher prevalence of comorbidities, lower immune response, and lower access to healthcare resources among older populations [17,36]. Therefore, our study suggests that life expectancy is an important factor to consider when designing and implementing public health measures and policies to prevent and control COVID-19.

Our results also highlight that population density has no major impact either on transmission or death rate increase in countries globally. This is contrary to the common assumption that higher population density facilitates the spread of infectious agents by increasing the contact and exposure of individuals [1]. However, this finding is in line with some recent studies that have found no significant effect of population density on disease transmission or death rates for COVID-19 [15,37,38]. This may be explained by the confounding effects of other factors, such as mobility patterns, social distancing measures, testing capacities, and healthcare resources [37]. Moreover, population density may not capture the heterogeneity and complexity of human interactions within and between different groups and settings [1]. Therefore, our study suggests that population density is not a reliable indicator of COVID-19 transmission or mortality and that more nuanced models are needed to account for the diversity and uncertainty of this factor.

Another important result of this study is to capture the outsiders’ impact on the transmission of COVID-19. The data were captured based on the export-sharing index globally and the amount of tourism. We have a significant result that the country whose global export-sharing index is more than or equal to 0.3 has significant chances of disease transmission. This is consistent with previous studies that have found a positive correlation between international travel or trade and infection rate for COVID-19 [39,40]. This may be due to the increased contact and mixing of different populations or sources of infection [1]. However, this finding is not conclusive, as some studies have found no significant effect or a negative effect of outsiders’ effect on disease transmission [41,42,43]. Moreover, outsiders’ effects may not capture the variation and uncertainty of different modes or routes of transmission, such as air, land, sea, or animal [1,41,42]. Therefore, our study suggests that outsiders’ effect is a relevant but not sufficient predictor of COVID-19 transmission and that more detailed models are needed to account for the diversity and uncertainty of this factor.

Our FIS model is based on the fuzzy logic theory, which can handle the vagueness and imprecision of the factors and the non-linearity and uncertainty of their relationships by using fuzzy membership functions, fuzzy operators, and fuzzy reasoning [3]. Fuzzy logic has been used in many areas like automatic control, banks, hospitals, and academic institutions [3]. Our study is one of the first to apply a fuzzy logic model with weights derived from statistical tests to estimate the chance of transmitting COVID-19 in a region/state based on four input parameters: outsiders’ effect, life expectancy, temperature, and others. Our study contributes to the existing literature on the factors of infectious agent transmission and the applications of fuzzy logic models to diagnose or predict infectious agents.

7. Conclusions

This study explored the factors that influence the transmission of COVID-19 across 95 top-affected countries. We found that the global export index, which reflects the exposure to foreign visitors or products, was positively associated with the infection rate. On the other hand, the population density, which reflects the contact frequency and intensity among individuals, was not a significant factor. Based on these findings, we developed a fuzzy inference system that can estimate the transmission rate of COVID-19 based on five input parameters: temperature, population density, life expectancy, smoking index, and outsiders’ effect. Our fuzzy inference system can provide a flexible and intuitive way to model and analyse the factors of infectious agent transmission and to estimate the infection risk in different settings.

Future Work

This study has some limitations that can be addressed in future research. First, we used the global export index and tourism index as proxies for the outsiders’ effect, but there may be other indicators that can better capture the exposure to foreign sources of infection. Second, we included an unknown variable ‘others’ in our fuzzy inference system, which represents the uncertainty and complexity of the infection process. The nature and impact of this variable need to be further investigated and clarified. Future research can also extend our fuzzy inference system to other infectious agents or regions and compare its performance with other models or methods.