key: cord-0851416-eqchbsgb
authors: Lawal, Olumide Mohammed; Vincent, Olufunke Rebecca
title: A two-level deterministic reasoning pattern to curb the spread of COVID-19 in Africa
date: 2021-05-21
journal: Data Science for COVID-19
DOI: 10.1016/b978-0-12-824536-1.00017-4
sha: a0793e96f7ff9f950ac8e8e179f14ea7729b0ca9
doc_id: 851416
cord_uid: eqchbsgb

The emergence of the pandemic disease COVID-19, which keeps many nations on their toes to find a the solution for a cure, needs a more predetermined approach by investigating the pattern and speed with which the disease is spread from one individual to another. The predetermining method can also be used to solve the future occurrence of such diseases. The predetermined approach is s good reasoning model for proactive measures. This study presents a two-level deterministic reasoning model to curb the spread of COVID-19 in some populated and economically optimistic African countries. A Petri net was used as a predetermining model to ensure proactive measures for present and future control of the spread of deadly diseases such as COVID-19. Data were collected from a reliable organization, and the result of the use the normal distribution model on these sets of data was fed into the Petri net to determine the severity and rate at which people contract disease before and during lockdown in selected countries. The results from this model proved that the number of cases of COVID-19 is not a function of the death rate in the selected countries; the discharge rate had a stronger effect on the COVID-19 cases. The results of the normal statistical distribution of various instances of COVID-19 were compared with those of the Petri net and proved that the hybrid deterministic model is viable for future use on any pandemic disease.

which it is implemented [21, 22] . The Petri net was simulated with the Monte-Carlo simulation framework to ascertain its viability and performance over other time-based Petri net models. Moreover, the bowtie model was used to check the results of the proposed Petri net model by analyzing the risks involved. The model was then suggested to have made the initial condition of an asset for which it was used distinctive against a well-known approach of the bowtie model in assessing the operation of the asset [23, 24] .

An optimization algorithm was used to extract information and execute the cast and time for a business process. It achieved a highly rewarding result, and a genetic algorithm was merged with the colored Petri net to extract further information from the business process. The obtained data were laced with some resource schemes of the genetic algorithm [25e27] . The result of the simulated model was analyzed on the genetic algorithm population and was fit for ranking and calculation, selection, mutation, and crossover operators until the specific predefined difference was observed [28e31]. This enabled a business process with a high desire level, resulting in allocation of the scheme.

Another model was developed with a colored Petri net. The model was seen to be flexible with the modeled variable. The colors were used as a token to solve the complex system for service and supplies [32] . However, the graphic potential showed that it was suitable for supplier selection, despite the ease of implementing the algorithm. The response time of the algorithm was slow when it was used with more than 50 type of supplies. The model was also good for future research when artificial intelligence techniques were built with it. Also, fuzzy logic was used to boost the performance of the model and proved that quantitative analysis was optimized for logic and linguistic rules [33, 34] .

According to another perspective, functional programming of a high order with Petri net could provide an excellent semantic business process for business process modeling that is different from object-oriented semantics [35] . The behaviors prove useful primarily when related they are to Haskell language, which is beneficial because it helped develop a generator that translates business processes automatically into a functional programming model [36, 37] . This model is more complicated but useful and efficient when it is used as a simulator on a graphical user Interface. Then, functional programming and object-oriented programming were compared for the benefit of the adjoining Haskell language.

Petri net modeling and optimization are aimed at creating a system that increases knowledge awareness, such as a case of pandemic disease. In addition, this Petri net model is built on devising ways of reasoning, which entails building a real-time process based on interactions between interdependence with prior knowledge in space [38, 39] . Petri net deals with undecidable but desirable uncertainties with true or false in the embedded statistical distribution model [40, 41] . Also, ideas that are outside the designer's knowledge background, together with organized knowledge to clarify new ideas, were designed to solidify the theory that is considered viable compared with the rest [42] .

This study presents a modified Petri net model based on a two-level deterministic pattern to curb the spread of the pandemic, COVID-19. COVID-19 data were analyzed and modeled in the Petri net to detect the rate at which people contract the virus. The spread of COVID-19 is modeled with the Petri net and normal distribution as a two-level reasoning pattern to curb it. Six countries in Africa (Nigeria, South Africa, Egypt, Kenya, Morocco, and Tanzania) were considered to be case studies. The data include suspected cases, confirmed cases, deaths, and discharged cases and were modeled to forecast future pandemic diseases.

The spread of COVID-19 is modeled with the Petri net and normal distribution as a twolevel reasoning pattern to curb the spread of disease. Six countries in Africa (Nigeria, South Africa, Egypt, Kenya, Morocco, and Tanzania) were used as case studies, and the data of different cases of COVID-19, which had details about the confirmed cases, deaths, and discharged cases, were modeled to forecast possible future pandemic diseases. Data for suspected cases were used as universal data from which death and discharge data were sieved from the raw data collected [43, 44] . This work first classified the raw category of data by checking for the rate at which the three incidences occurred with the Petri net. On this basis, the average rate of the three occurrences were known for normal flow or transition in the general incidence occurrences [45, 46] . This flow produces the two main Petri net diagrams for statistical generalization of the occurrence of COVID-19 incidences. The result of the transition in the Petri net suggested the various types of behavior and spread of COVID-19 among people. Whereas the statistical normal distribution suggested various ways in terms of numbers, COVID-19 spreads among people. The patterns of the data for each country are represented as random variables after the data were classified to fit into function f n , which results in a normal distribution of 1 and a normal distribution whose mean is 0, because normal distribution is useful in statistics and in many applications. Thus, function f n is determined by analyzing the growth and changes in data from relevant institutions [47] .

The rescue to discharge is a representation of the transition function of what happens between the time the disease is confirmed and the discharge or death of patients. The spread of recoveries is also relevant to curbing the pandemic. To ensure that the rescue and discharge of COVID-19 patients are met at the expected time and manner, Fig. 30 .1 represents a running process for handling COVID-19 pandemic disease for any case. If we consider the COVID-19 suspected cases to be that of patients in any location, or in diagnostic center, which could be a quarantine center or a hospital and suppose a suspected patient initiates the rescue process by calling a medical rescue center, a response is expected from the clinical team. In this situation, two possible outcomes are ensured at an interval of time. The rescue process may end on a positive or negative note, tagged as through or decline in the rescue initiation process. If the rescue request is declined, which happens rarely, the situation may result in increase in death rate. If the suspected patient eventually dies, the time of death and burial are recorded for evaluation as the process is terminated [48] .

On the other hand, if the rescue process is positive, the suspected patient then waits for a response at a time interval. The time of request and response are noted in the process. The patient is taken to the quarantine center or hospital for diagnosis and treatment. If the suspected cases are diagnosed as negative, patients are treated for other diseases. The time of diagnosis and treatment for different situations are recorded, and the patient is discharged as the process is terminated. Suppose the suspected cases are diagnosed with COVID-19; the patient is admitted to the hospital for treatment until he or she is discharged with the time recorded, and the process is terminated. If during therapy the patient dies, the death is arranged for burial immediately, with the time recorded, and the process ends [49] .

This process aims to predict the duration of time of the spread of COVID-19 and other related pandemic diseases, and the risk for breaching the deadline for handling the pandemic. The model has been evaluated against likely future occurrences and predicts the possible rescue process for future events using the elapsed time [45] . Fig. 30 .1 represents this transition from admission to discharge. 

A Petri net is often used to model a transition system, in which the state of the system is represented by placing and corresponding tokens; hence, the execution of the transition of Petri net measures the change in state. In modeling the incidence of COVID-19, some terminologies are essential in terms of states and how they change. Tokens represent the situation of COVID-19 cases in any environment; a transition represents the impact of infection from one person to another. Individuals infected with COVID-19 may interact with each other in a crowded environment. A place could be a pointer to another place to show an individual's correspondence, because the state of this individual can occur at least once. Moreover, after an individual has been contacted and cured, he cannot contract it or spread the disease. The resultant effect of one individual case may be from the incidence of another under certain conditions of safety lapses [46] .

Upon execution, the model is designed so that the token that serves as input in one place also serves as a pointer to another future event. As a result of these changes in Petri net behavior, the consequence of the transition of incidence is analyzed for future occurrences of any severe event of such a pandemic. Using two environments as an example, when an incidence of COVID-19 takes place in environment A, the transition has a ripple effect on another individual as a result of inadequate safety measures. Therefore, it may result in another incidence in environment B. Fig. 30 .2 expresses the Petri net transition analysis of pandemic behavior, in which pðiÞ indicates COVID-19 incidents in one situation, pði þ1Þ is shown as resultant lapses of the previous environment, and pðnÞ points to later COVID-19 cases. In Fig. 30 .2, i is an index with the initial state for a token pðiÞ that shows a COVID-19 incidence that took place in environment A. Transition tðiÞ indicates the impact of COVID-19 incidents at environment A on environment B, and tði þ1Þ represents the damage that environment B would cause the next environment pðnÞ, where i 1 [50,51].

Petri nets are mathematical modeling tools used to analyze and simulate COVID-19 cases by considering the cause and flow of transmission in terms of the increasing number of patients in different environments. This study modeled the circumstances of two linking nodes that serve as the place or situation in which the pandemic disease takes place within a particular country. This set of places and objects, and the set of Eq. (30.1) represents a Petri net behavioral transition of the disease, patients, and environment, where P ¼ fp 1 ; p 2 ; . p n g is a set of cases associated with COVID-19 and T ¼ ft 1 ; t 2 ; . t n g is a set of transitions around the COVID-19 case. I is an input function such that ðP ÂT Þ/N , where N is a positive set of integer numbers. The scaler, Iðp; tÞ, is the interactive behavior that exists between place p and transition t, in a forward direction. At the same time, O is an input function such that ðT ÂPÞ/N . Scaler Iðt; pÞ, is the interactive behavior that exists between place p and transition t in a backward direction [52] . Now, M/N is the marking that exists in the proposed Petri net. The number of places, n  1, for the incidence of the COVID-19 represented by the vector in each environment is tokens represented in the form of a circle with dots place inside it. The first marking is represented as M 0 , which is always at the initial state in the Petri net model, whereas M is used over place p i . In the Petri net, a circle represents places whereas transitions are represented with a rectangle. The direct line represents the arcs whereas tokens take the form of dots. The number of directions shows the execution of the Petri net. Suppose ðà t Þà p is the input places of transition t and t à ðp Ã Þ is the output places of transition t. Then, these two rules determine the execution of the Petri net that shows that t was enabled at marking M as it changes form to marking M 0 . Hence,

where a is the number of arcs from transition t to place p i and b represents arcs from place p j to transition t [53] .

Input function I : P  T /ð0; 1Þ is the arc from place p to transition t, whereas output function O : T  P/ð0; 1Þ shows the arc from transition t to place p. Also, mapping M : P/ð0; 1Þ is the marking of a Petri-net. Place p can have 1 token. Function f n for t is used to show that an enabled transition can be executed and meets the conditions for tokens to take effect on its input places. The enabling rule for transition t of a Petri-net takes effect in marking M: If Mðp i Þ > 0, then p j εt à and f n ðtÞ ¼ true and M À p j Á ¼ 0, for p j εt à . Thus, when the execution or firing rule for transition t fires, marking M of the Petri-net

To determine enabling function f n for the transitions, the normal distribution is fed into the modeled Petri net, because a normal distribution is useful in statistics and is employed in many applications. The pattern of data for each country is represented as random variables after the data have been classified to fit into function f n , which results in a normal distribution and normal distribution whose mean is 0.

Because the standard deviation is 1 for the statistics of the data, the density function becomes comparatively smaller. According to the standard, the data distribution was calculated to achieve a goal by classifying the data to represent the transition, and the mean and variance were determined by using parameters m and l, and variable Z with 0 and 1. Thus, function f n is determined by collecting real and growing COVID-19 data from relevant institutions. The transition for a case is a pointer to the next case with the same distribution, so that enabling function f n is given as: In Eq. (30.2), DISTRða; bÞ is a function to generate 20 cases across six selected countries, in which the average total death rate in a week satisfies the normal distribution with values for a and b fed into the Petri net [55, 56] .

The data represent the condition of COVID-19 cases, the death rate, and the discharge rate in six different countries in the African region. These countries include Nigeria, Egypt, South Africa, Morocco, Kenya, and Tanzania, which have a high level of international economic optimism and a growing population pattern. The death rate and the discharge rates are sieved from COVID-19 cases in each selected country by taking a class of 10 cases inclusive for statistical distribution every week since it started in these countries. The cases are represented as the place in the distribution for the Petri net, in which the number of deaths in the classes or places in the Petri net is recorded as the transition for each country in Table 30 .1. Figs. 30.3 and 30.4 describe the first and second models of the COVID-19 death rate management in an interactive and separate mode. The first model showed that the interaction of the infected individual would have resulted in a more devastating effect on the selected society at large if the spaces existing within them were considerably small, unlike the separate interaction ensuring that transmissions of the pandemic diseases were managed in their respective countries. Space and time management in this scenario include interpersonal connectivity at an interval of time; these were maintained as the closure of the international airport at a particular expected time as well as closure of the land border at a scheduled time. The transition concerning the place is represented in the respective countries. However, as much as the location and transformation are the same for each Petri net model of separate and interactive mode, the terminating places are different from their respective transitions [57e60].

For example, T1 and T4 have the same distribution of the different numbers of death, as shown in the flow of the Petri net after it was classified. The classification of data for the Petri net analysis and behavior was in line with the analysis for optimum use against any foreseen pandemic case in West Africa. In these classes, the death rate, suspected rate, and discharge rate of cases were analyzed with the Petri net before the final statistical normal distribution was used for the final data analysis, which is ultimately useful for future forecasts against any pandemic disease. Table 30 .2 explains the result of the Petri net analysis, from which the death rate and discharge rate were sieved. According to the total death rate of each country, Kenya took the lead, whereas Egypt and Morocco had the fewest deaths. The rate of flow of transmission was also represented as transition T for each selected country in West Africa at the time of analysis. The corresponding means and standard deviations of the death rate were calculated, which suggested that Tanzania and Kenya need to take more physical proactive measures. The death and discharge rate for each selected country are shown in Table 30 .3, which suggest that ultimately, the death rate almost doubled the discharge rate for the total cases modeled in Fig. 30.3 . The economic activities of the chosen countries contributed to spread the diseases at the time interval before the land border and airport were closed and the total lockdown took place.

The emergence of the pandemic disease COVID-19, which keeps many nations searching for a cure, needs a more predetermined approach by investigating the pattern and speed with which the disease is spread from one individual to another. According to Fig. 30 .2, the general reasoning pattern of solving COVID-19 cases with a Petri net is a model that helps sieve the survival and death cases from suspected cases, in which a suspected case, P, could result in multiple instances if the chain of transition t is unbroken. However, if there is a break in interactive behavior between P and t in the case, provision Pði þ1Þ and tði þ1Þ in the general reasoning pattern is provided for an immediate correction in the flow.

Open data from a different source, in social media and in a well-organized society and government, were used to model the accuracy of the research results of the Petri net; the model from which these data were fed were assumed to be useful for future purposes. Much-expected data after the pandemic subsides will be helpful for research to enable our environment to become safer and restored, and to grow in the future. This predetermining method can also be used to solve the future occurrence of such diseases. The predetermined approach is as good as a reasoning model for proactive measures. Thus, the Petri net was used as a predetermining model to ensure proactive measures for current and future control of the spread of deadly diseases such as COVID-19. To strengthen the Petri net argument for COVID-19, enabling function f n for transitions, the normal distribution is fed into the modeled Petri net. In this work, function f n is determined by collecting real and growing COVID-19 data from relevant institutions. The transition to a case is a pointer to the next instance of that distribution.

The pattern of data for each country is represented as random variables after the data are classified as fit into function f n , which results in a normal distribution whose mean is 0, because a normal distribution is useful in statistics and is employed in many applications. The results of this general model are shown in Table 30 .1 and Fig. 30.4 . Whereas Table 30 .3 shows the average total number of death rates in a week, the probability of death across the four countries, with their respective average normal distribution, are shown in Table 30 .2 and interpreted in Table 30 .1 with the Petri net, against the normal flow of statistics for deaths and discharged cases in Table 30.3 . Results from this model proved that the number of suspected cases of COVID-19 is not a function of the death rate in the selected countries, but the discharge rate had a stronger effect on COVID-19 cases. The results of the normal statistical distribution of various instances of COVID-19 were compared with those of the Petri net; the results proved that the hybrid deterministic model is viable for future use for any pandemic disease. Moreover, this study presents a two-level deterministic reasoning model to curb the spread of COVID-19 in some populated and economically optimistic African countries.

This model shows that the projection for mitigating other pandemic diseases, as well as COVID-19 itself, will have a meager percentage, because the experience of every person who escapes the worst of COVID-19 should have suggested a new strategy curbing pandemic diseases in terms of deployment of biological and information technologies as far as the area is concerned. These technologies could inform individuals that the best approach to mitigate COVID-19 is based on analyzing information about it, and the best way to tackle this infectious disease is to analyze the previous incidence that might have taken place to solve current or future occurrences.

The awareness of the immediate closure of borders, adequate safety, and social distancing propagated through social media platforms, from the international and national communities to educate all levels of citizens in these countries shows that the number of cases needed some prompt actions. However, educational level and religion seem to show other discouraging factors, in that proper information about the growth of infection in these regions is not well-disseminated. Incentive programs might not have been in place to ensure adequate knowledge about the spread of COVID-19 and its impacts on the information age. Still, there have been some monetary donations to help ease the negative result of the "stay at home" campaign. In this situation, when COVID-19 incidences continue to grow and their number is increasing, there are available data in affected countries, both developing and developed.

This study has presented an improved Petri net model to analyze and curb the spread of the COVID-19 pandemic in African countries. The spread of COVID-19 is modeled with Petri net and normal distribution as a two-level reasoning pattern to curb the virus. Six countries in Africa (Nigeria, South Africa, Egypt, Kenya, Morocco, and Tanzania) were considered as case studies.

Data for the suspected cases were used universal data from which death and discharge data were sieved in the raw data collected. This work classified the first category of data by checking for the rate at which the three incidences occurred with the Petri net. On this basis, the average rate of the three occurrences were known for a normal flow or transition in the general occurrence of incidence. This flow resulted in the two general Petri net diagrams for statistical generalization of the occurrence of COVID-19 incidences. The results of the transition in the Petri net suggested various ways in terms of behavior and the spread of COVID-19 among people. Whereas the statistical normal distribution model suggested various ways in terms of numbers, COVID-19 spread among people. The pattern of the data for each country were represented as random variables after the data were classified to fit into function f n , which resulted in a normal distribution of 1 and a normal distribution whose mean was 0, because a normal distribution is useful in statistics and is employed many applications. Thus, function f n was determined by collecting real and growing COVID-19 data from relevant institutions.

Real data were gathered, studied, and modeled with Petri net to understand the rate at which people contracted COVID-19. The results from the Petri net suggests that some countries have a high rate at which people compared the extent of COVID-19 cases. Hence, two countries were suggested that high the rate social interactions might have caused increase in COVID-19 cases, though death rate would also increase. The Petri net result in Table 30 .2 showed that the weekly growing death rate of patients, which at some point normalized, had risen; this behavior was also compared among the four selected high economically optimistic countries. The rate at which the suspected case growth was compared with the death rate by the Petri net showed that future caution need to be considered regarding how to respond quickly to pandemic diseases as severe as COVID-19. This work also suggests that there is a need for individuals, organizations, and the government to scale up their information technology and telecommunications against regional and global pandemic diseases.

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