An Artificial Intelligence-Based Scheme for the Management of Vaccines during Pandemics ^†

Abstract

A pandemic like COVID-19 caused a massive blow to the global economy, and its impacts will be large and endure across all domains of life. One of the crucial factors in fighting this pandemic is the proper management and administration of the limited vaccines available. The objective of the proposed research is to apply an artificial intelligence approach based on fuzzy logic for the allocation of vaccines to state authorities by a central government. The objective is achieved by developing an artificial intelligence technique based on a fuzzy logic inference system that takes into account the population and the number of active pandemic cases to infer the proportion of available vaccine doses to be allocated to the states. This approach ensures that sufficient doses of vaccines are available in the states on priority where the proportion of the spread is higher and vaccines are not wasted in states where the proportion is lower. The proposed scheme is simulated using MATLAB. The results showed that the proposed artificial intelligence-based approach can ensure proper distribution of the available vaccine doses to the states and enhance the fight against pandemics.

1. Introduction

Pandemics like COVID-19 have resulted in wide-ranging morbidity and divested economies worldwide. It has created a global health crisis, and the pandemic has created cultural and geographical intolerance. The pandemic is far from over and is predicted to continue its onslaught in the coming days [1,2,3,4,5,6]. Vaccines are one of the most effective tools for protecting people against pandemics [7,8,9,10]. In the annals of public health, the worldwide endeavor to generate vaccinations safeguarding against pandemics has been unparalleled. By the end of 2020, a small number of vaccinations were created and approved by the government. The vaccinations were distributed beginning in December 2020 in accordance with several distribution strategies, which were primarily determined by the moral standards of equality and fairness [8]. The allocation criterion will be expanded as new products are approved, and vaccine manufacturing ramps up to the point where the supply permits vaccinations to be used widely. Even while vaccination campaigns have begun in practically every nation, officials are still having trouble overseeing the administration of vaccine distribution to various sites. Ensuring sufficient quantities of vaccines are distributed quickly, efficiently, and equitably will be critical [9,10].

The traditional method of distribution of pandemic vaccines by a central government or authority is to allocate the number of vaccine doses based on the population of the state. This has two disadvantages. The states having a severe number of active cases may face a shortage of vaccines, resulting in super spreading, and the states having fewer active cases may waste vaccines because of negligence to take vaccines due to a feeling of pseudo-security. Hence, the priority in terms of the number of active pandemic positive cases in the state also has to be considered to avoid the wide spread or super spread of the virus in those states with a severe number of active cases [7]. However, there are no strict and hard rules or proper mathematical models to define the relationship between inputs and output, as they are uncertain, but there are approximate rules based on human reasoning [11]. Fuzzy logic is a soft computing tool for embedding structured human knowledge into possible algorithms and providing models for human reasoning modes that are approximate in lieu of exactness [12,13,14,15,16,17,18,19,20,21]. This approach ensures that sufficient doses of vaccines are available in the states on priority where the severity of the spread is higher, and vaccines are not wasted in states where the severity is less. It ensures proper distribution of the available vaccine doses to the states and enhances the fight against pandemics. Traditionally, the vaccines are distributed uniformly to different regions without even considering the population in pandemic situations like COVID-19. The number of active cases and population are different in different regions where the population and number of active cases are high; the vaccination campaign has to be conducted at a higher rate to avoid the rate of spread from increasing further. This can be accomplished by allocating a larger proportion of available vaccines in the regions where the population and active cases are higher. Hence, the allocation of vaccines has to be optimized to contain the spread of the virus.

2. Methodology

The concept of FL (fuzzy logic), an artificial intelligence tool, was presented by Dr. Lofti Zadeh of UC/Berkley in the 1960s. It behaves like a function of uncertainties of natural languages [18]. Basically, the FL-based system presents a system which deals with human reasoning modes, and due to uncertainties and human reasoning, the generated outputs are not exact but are a close approximation. Due to reasoning, FL system application can be extended to designing intelligent or smart systems, and the basis for such system designs is the knowledge expressed in human languages. With respect to areas of human activity, almost everywhere we can see the application of intelligent systems. We can see them everywhere because these systems can compute both numerical as well as symbolic information [12]. Figure 1 depicts the fuzzy inference system.

In general, we have two states in the logic system: high–low or yes–no. However, human thinking does not lie between two states because uncertainty is an important factor in human thinking; thus, fuzzy logic is designed to deal with uncertainty [12,16,20,21,22,23]. The fuzzy set is non-identical to general set theory, which is based on Boolean algebra. In general set theory, we have only two logic states: 1 or 0. Operations like logical NOT, logical OR, and logic AND are also applicable for FL systems [18]. The basic functional block diagram for an FL inference system is shown in Figure 1. Fuzzy logic is an AI technique which mimics human reasoning, and hence, it incorporates human reasoning into the computing system, in this context a computation based on the population and number of active cases [21]. The number of vaccines to be distributed based on these two inputs does not have strict and hard rules for computation, but rather, approximate rules based on human reasoning. The rules are of the following type. If the number of active cases is high and the population is high, the proportion of vaccine to be distributed is “high”. If the active cases are low and the population is low, the proportion of vaccines to be distributed is “low”. This type of human reasoning can be incorporated in computing using fuzzy logic.

2.1. Fuzzification

Since the input consists of two-state logic data, the FL inference system cannot process this input directly, so a fuzzification block is used to transform this scalar logic value to a fuzzy quantity. This fuzzification is performed by introducing a membership value to each input section. To transform real logic into the appropriate fuzzy quantity, certain data are required. These data are provided by a knowledge base block and the data in this block are stored in the form of membership functions.

2.2. Knowledge Base

We can split the knowledge base block into two parts. The first part is the data base and the second one is the rule base. As the names indicate, the data base holds the data required to process or transform the real-world scalar logic state to a fuzzy quantity. For transformation, this block utilizes membership functions. Once the fuzzy data are processed, a reverse transformation is used for defuzzification, and this output is now suitable for real-world application. On the other hand, the process must be carried out using sets of rules generated from systems knowledge, where rules are provided by rule bases encompassing conditional statements like IF, THEN, logical statements like AND, OR, etc. The knowledge base is analogous to the human brain, because without the knowledge base, the FL system cannot exist. These blocks are designed carefully and need expertise in systems into which fuzzy logics are incorporated [16,18,19,20].

2.3. Fuzzy Inference Engine

The process which utilizes FL rules from the knowledge base block for transforming fuzzy input to fuzzy output is called fuzzy inference. These days, we can generally see three types of FL inference techniques, namely Sugeno-Type Inference, Tsukamoto-Type Inference, and Mamdani-Type Inference [18]. Figure 2 shows the entire process of and the block diagram of the methodology.

2.4. Defuzzification

The process in which reverse transformation takes place is called defuzzification. The generated output of the inference engine is in a fuzzy form, since real-world systems can accept only Boolean logic or two-state logic. Hence, this output must be transformed in such a way that the real-world systems can deal with it. The centroid method is a popular technique used in the defuzzification process. An aggregated fuzzy output is the basis of the centroid method, i.e., before defuzzification, a max operator is used for aggregating all FL outputs based on different rules from the rule base [18].

3. Fuzzy Logic Inference System for Allocation of Pandemic Vaccines

The two input variables, population and number of active cases, are normalized into the range [0, 1] by appropriate scaling factors. The normalized population and the normalized number of active cases are the inputs to the fuzzy interface system. The proportion of vaccine doses, normalized in the range [0, 1], is the output. The inputs are fuzzified using triangular membership functions, as shown in Figure 3 and Figure 4. In this research work, the decision on proportion allocation of vaccines to a particular region is based on a Mamdani-type fuzzy inference system, with population and number of active cases as fuzzy inputs and the proportion of vaccine to be distributed as the fuzzy output. Each rule in the Mamdani system of reasoning has a premise, which is a statement with the whole and the active cases connected by the conjunction “and”; the correct value is then applied to the corresponding fuzzy set of vaccines in different regions. Then, the fuzzy output corresponding to the different rules is aggregated using the “max” operator and defuzzified to give the final output of the specified “vaccination percentage”. As a result, the “min” fuzzy fuzz is applied to the member values of the input to obtain the correct value of the rule.

Incorporating the informed search approach, the methodology involves several interrelated steps. Beginning with data collection and normalization of variables such as population and active cases, it utilizes fuzzy logic for fuzzification, associating input values with linguistic terms via triangular membership functions to capture nuanced states. Concurrently, a set of expert-derived rules connects fuzzy input values to the desired vaccine allocation output, aggregating the fuzzy output to determine the fuzzy output of the proportion of vaccine allocation and defuzzifying the fuzzy output to a crisp output of the proportion of vaccine allocation.

The rule bases of fuzzy inference systems using approximations of human reasoning are given in

Table 1. Rule base.

Population/Active Cases	L	M	H
L	VL	L	M
M	L	M	H
H	M	H	VH

, and the fuzzy surface showing the relationship between inputs and output is shown in Figure 5.

Mamdani-Type Inference is proposed. In Mamdani inference, each rule has a compound statement in its predecessor using the conjunction “and” and a fuzzy set in its consequence. For example, one rule is “The vaccine dose is VH if the population is H and the number of active cases is H.” Since “and” is the connector, the fuzzy operator “min” is used on the member values to obtain the actual value of the rule. The resulting fuzzy set then obeys this truth value. As shown in Figure 6, a rule base with rules of type “R_i: If x is A_i and y is B_i, then z is C_i” is put into practice. The final sharp output is obtained by defuzzifying the corresponding fuzzy outputs with different rules, which are then aggregated using the max operator.

We have utilized the centroid method because it generates highly precise and smooth outputs; we can calculate the defuzzified value by using the following integral Equation (1).

$$z*=\frac{\int {\mu }_C\left(z\right).zdz}{\int {\mu }_C\left(z\right)dz}$$

(1)

Here, z* holds the defuzzified value, and z indicates the output variable, $\int {\mu }_C\left(z\right)$, the membership function of the aggregated fuzzy output. Rules connect these terms to dosage allocations, capturing the complexity of pandemic severity [24]. By evaluating these rules with real-time data, fuzzy inference determines precision by accurately considering both the population and number of active cases. Fuzzy logic helps avoid over-allocating doses in regions with low transmission and under-allocating in high-transmission areas. This balanced approach ensures that each dose is used effectively and that no region faces a shortage or surplus that might lead to wastage.

4. Fuzzy Logic Inference System Simulation for Allocation of Pandemic Vaccines

For simulation-based study of the performance of the proposed scheme, it is assumed that vaccines have to be allocated to six states A–F, where the normalized population and normalized number of active cases are as shown in

Table 2. Input parameters.

State	Population Normalized	Number of Active Cases (Normalized)
A	1	1
B	1	0.5
C	0.5	1
D	0.1	1
E	0.1	0.1
F	0.01	0.01

. The proposed fuzzy inference systems are simulated using MATLAB R2023b, and the results are shown in Figure 7, Figure 8 and Figure 9.

The proposed system is simulated using MATLAB and the results are compared with the analysis using human reasoning.

Table 3. Doses of vaccines allocated.

State	Doses of Vaccines Allocated (Normalized)
A	0.92
B	0.75
C	0.75
D	0.56
E	0.258
F	0.11

shows the results that the vaccination allocation is higher for regions with a higher population and a higher number of active cases. The allocation is lower for regions with a lower population and fewer active cases. The utilization of fuzzy logic allows two considerations, size of population and number of active cases, characterized as “very low”, “low”, “medium”, “high”, “very high”, etc., as in the case of normal human reasoning. This allows the optimal allocation of limited vaccines available.

5. Conclusions

In this research, artificial intelligence based on fuzzy logic is proposed for the allocation of vaccines from a central government to state authorities. The fuzzy logic inference system considers the population and number of active pandemic cases for inferring proportions of available vaccine doses to be allocated to states. This approach ensures that sufficient doses of vaccines are available in the states on priority where the proportion of the spread is higher and vaccines are not wasted in states where the proportion is less. The proposed method is simulated using MATLAB. The results show that the proposed approach ensures proper distribution of the available vaccine doses to the states based on the population and the number of active pandemic cases and enhances the fight against the pandemic.