1 Introduction

COVID-19 first came into light on December 31, 2019 as a deadly disease in Hubei, China [1]. It was classified as a pneumonia case of unknown cause. It belongs to Severe Acute Respiratory Syndrome (SARS) based on disease behavior. Originally, COVID was introduced by Tyrell and Bynoe in 1966 [2]. According to Tyrell and Bynoe, SARS viruses are alpha, beta, gamma, and delta. Bats, birds, and pigs are the main sources of these viruses. Infection with this virus causes a variety of symptoms, sneezing, cough, fever, congestion in nose, runny nose, pain or irritation of the throat and diarrhea fever. The first appearance of the new coronavirus occurred in the southern region of India in January 2020. Due to the presence of the novel coronavirus worldwide, the WHO has declared it a pandemic [3]. Corona virus spread leads to increase of the number of COVID patients rapidly. A person infected with this virus can infect other healthy people by coughing or sneezing. So far, many variants of the novel coronavirus have emerged, including Delta and Omicron. Latest COVID variants include the BF 7 variant (a new variant of Omicron). Upper respiratory tract is affected due to virus and causes symptoms such as vomiting and diarrhea. It is intended for people with weak immune systems. BF 7 emerged from China in October 2022. Cases have also been found in India. The new coronavirus remains in the human body for an average of 10 days, which corresponds to the incubation period of the new coronavirus [4]. During this time, the patient can infect others. Infection can be delayed through the use of non-pharmaceutical interventions (NPIs) such as: For example, social distancing, avoiding large gatherings, wearing masks, closing schools and universities, adopting work-from-strategies, washing hands frequently, and isolating patients. However, models need to be developed to predict the number of cases so that necessary precautions can be taken. In the current work, a novel fractional model is being developed for analyzing viral spread scenarios.

Mathematical models have proven to be the best predictors when the spread of the virus is ambiguous [5]. These models showed excellent performance in estimating virus scenarios. The model has the flexibility to be modified to incorporate real-world parameters such as social distancing, frequent hand washing, and mask wearing during the COVID-19 pandemic. Susceptibility-infection-removal (SIR) and susceptibility-exposure-infection-removal (SEIR) are common mathematical models for early prediction of viral spread. These models have been found very much suitable for predicting the spread of viruses such as the plague. These models are flexible and can be adapted to new parameters. Many models have been developed in the literature using new parameters such as incubation period, exposed population, and human births and deaths within the population. These models use Euler’s ordinary differential equation (ODE) to solve the problem of disease prevalence. ODE uses an integral calculation, which has been found to be an inaccurate approximation of the scattering function [6].

In the current work, fractional calculus is being used to solve ODEs [7]. Fractional calculus has non-local memory characteristics [8] due to which function approximation is more accurate. Mathematical models based on fractional calculus were combined with machine learning models for cancer detection and classification [9,10,11,12,13]. In this work, a novel fractional mathematical model has been devised for the early estimation of COVID spread.

1.1 Literature Review

COVID spread scenario has been analyzed by many machine-learning models. For survival and death cases of critically ill COVID patients, Wong et al. devised XGBoosting prediction model [14]. The authors of this study used data from the United Kingdom Biobank (UKBB). Two experiments have been conducted for the investigation. The study’s author identified five key risk factors, including multiple comorbidities, cardiometabolic disorders, age, obesity, and impaired renal function, that had a significant impact on case prediction. A model employing Support Vector Machine (SVM) has been put out by Sun et al. for predicting patients who will be severe and those who won’t [15]. They included the percentage of feature clusters of differentiation 3 (CD3), Age, immune system, total protein, and growth hormone secretagogues (GHSs) are considered to be the most significant factors in identifying patients as severe or not severe. The accuracy in classifying patients was found to be 75%. The involvement of machine learning in the COVID crisis has been published by Syeda et al. and Heidari et al. [16, 17]. They claimed that machine learning made a significant contribution to COVID prediction. The SVM classifier has been utilized in another study by Yao et al. to categorize patients according to the severity of COVID patients based on symptoms [18]. The findings showed that 32 factors have strong connections. They discovered that the two factors that have the biggest influence on how severe and mild cases are classified are age and gender. Additionally, reports indicate that male patients are said to be higher risk of acquiring COVID severity. Logistic regression based model developed by Hu et al. to analyze the severity of patients suffering COVID [19]. The found four features namely D-dimer level, lymphocyte count, age, and sensitive C-reactive protein level as primary among many features and these features have been seletected to train the classification model. In order to forecast the death of COVID patients, Bert- simas et al. applied the XGBoosting machine learning model [20]. To develop the machine learning model for their research, demographic and clinical variables were taken into consideration. According to Mahdavi16, Snchez-Montas et al. utilized a machine learning model based on linear regression to predict the death of COVID patients [21]. Age and oxygen saturation were cited in the study as important variables in predicting patients’ mortality. Similar techniques have been tried to forecast COVID-19 cases, including Lasso regression, SVM (Linear and RBF), Random forests, and KNN [22]. International Labor Organization of Egypt [23] has conducted a case study. Regression modelling was employed in the study to forecast COVID instances.

Dharapanani et al. proposed a machine learning technique for predicting novel coronavirus patients. They have used dataset provided by Israel Albert Einstein Medical Center in São Paulo, Brazil to carry out experimental work [24]. They used ensemble techniques based on begging and boosting to devise novel model. The results obtained have been compared with other model using confusion matrix, ROC curves and confidence values. In the observation, they reported that the random forest technique is providing highest training and validation accuracies of 97% and 95%, respectively. Rohini et al. have devised machine learning model to predict novel coronavirus cases [25]. Their approach formed the origin of the disease as a basis for predicting the COVID cases. The ANN approach yielded 98% accuracy. DK Sharma et al. devised a support vector machine (SVM) based model to predict COVID-19 [26]. They used mRMR (Minimum Redundancy Maximum Relevance) as a modified Cuckoo search optimization strategy to improve the performance of his SVM using an advanced feature selection framework. Choudary et al. [34] devised machine learning models to identify the presence of COVID-19 patients. They found an accuracy of 98.38% using the SVM algorithm, but the XGBoost model outperformed the best with a high recall of 99.26% without sacrificing accuracy of 97.71%. Tiwari et al. used classical machine learning techniques to analyze COVID-19 transmission trends, treatment rates, and mortality [27]. In their study, they found the Nave-Bayes classifier as most promising technique. Lai et al. used a rule-based ensemble technique to predict mortality in COVID-19 patients [28]. They achieved higher accuracy with value 86.9% and F1 coefficients with value 71.6%, respectively. Shi et al. devised attention-based neural network model to chest radiographs to predict COVID cases [29]. Using the hybrid attention frame, they achieved an accuracy of 94.11. Zhang et al. Using the CNN framework to create a custom model, they identified COVID from CT images [30]. They found an accuracy of 96.32 and an F1 score of 96.33. Karaibani et al. [31] used CNN technology to find patients with COVID-19. They found prediction accuracy for new coronavirus patients is 99.4. Pi et al. used an image processing technique with a neural network model based on extreme neural learning to distinguish between chest images of healthy and COVID-19 patients [32]. In their study, they used K-fold validation technique and achieved a classification accuracy of 76.98%.

A literature survey summary has been tabulated in Table 1.

Table 1 Literature survey summary of the COVID prediction models
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It has been found on the literature review that most of the authors are using machine learning approaches for spread prediction. Machine learning models are able predict cases on presence of the historical data. These historical data are helpful in training of the model. But as COVID emerge as deadly disease and historical data was not present. In such scenario, only mathematical model can be used to predict cases since these mathematical models does not require historical data. Hence, in the current work, fractional model has been proposed for prediction of COVID disease. The models not only applicable to COVID but can be applied.

The organization of the current study includes Sect. 2 in which the designing of a mathematical model for COVID prediction has been provided. The results analysis is presented in Sect. 3. Theoretical contribution and implications for practice have been provided in Sect. 4.

2 Proposed Methodology

The COVID epidemic scenario can be described using mathematical modeling with eight different compartments [34]. The model contains various compartments. That is, the vulnerable compartment S(t) gives the population potentially infected with time t, while the exposed compartment E(t) gives those who came into contact with infected COVID patient but who have no symptoms. Infectious compartment I(t) gives the list of individuals with symptoms of the disease, A(t) is the list of asymptomatic individuals, Q(t) gives the list of quarantined individuals, R(t) gives list of recovered people, D(t) enlist of dead people,

T (t) is a list of protected peoples. The proposed model is presented in the Fig. 1 [34].

Fig. 1
figure 1

Spread scenario of COVID

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All the compartment described above can be mathematically defined as:

$$\frac{dS(t)}{dt}=-\frac{\beta (S\left(t\right)I\left(t\right)+q(A\left(t\right))}{N}-\Omega S(t)$$
(1)
$$\frac{dE(t)}{dt}=\frac{\beta (S\left(t\right)I\left(t\right)+q(A\left(t\right))}{N}-\eta E\left(t\right)$$
(2)
$$\frac{dI(t)}{dt}=\rho \eta E\left(t\right)-\gamma I(t)$$
(3)
$$\frac{dA(t)}{dt}=(1-\rho )\eta E\left(t\right)-\gamma I(t)$$
(4)
$$\frac{dQ(t)}{dt}=\gamma (I\left(t\right)+A\left(t\right)-\lambda \left(t\right)Q\left(t\right)-k\left(t\right)Q\left(t\right))$$
(5)
$$\frac{dR(t)}{dt}=\lambda \left(t\right)Q(t)$$
(6)
$$\frac{dD(t)}{dt}=k\left(t\right)Q(t)$$
(7)
$$\frac{dT(t)}{dt}=\Omega S(t)$$
(8)

Here, S(0) > 0, I(0) > 0, R⋯0, D⋯0, T⋯0, E(0) ⋯0, Q(0) 0, and.

N = S + E + I + Q + R + D + T . In the Eqs. (1–8), some symbolic constants have been used which are described in the Table 2.

Table 2 Computer configuration
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The Eqs. (1–8) are Ordinary Differen- tial Equations (ODEs). In the equations, many symbolic parameters have been used such as Ω which us protection rate, η is Inverse of average latent time, γ represents quarantine rate, β is infection rate, N is the total population, λ(t) is the time dependent recovery rate and κ(t) is time dependent Mortality rate. The change in susceptibility to disease is presented by Eq. (1). It depends on infection rate β and defense rate omega. Equation (2) approaches the changes over time in exposed colonies. A person who is infected but not yet contagious is considered exposed. It depends on the infection rate β and the incubation time η. A high β increases the number of people belonging to the exposure category. Equation (3) represents change of infected peoples. It protection rate Ω, incubation period η and Probability of symptomatic infectious ρ. Equation (4) represents change of asymptomatic peoples.

It also It protection rate Ω, incubation period η and Probability of asymptomatic infectious (1–ρ). Equation (5) represents change of quarantined peoples. As it can be seen visually from figure 1 that it combines both infect and asymptomatic peoples. It depends on mortality rate k, recovery rate λ and Quarantine rate γ. Equation 6 represents change of recovered peoples. It depends on recovery rate λ. Equation (7) represents change of death peoples. It depends on mortality rate κ. Equation (8) represents change of protected peoples. It depends protection rate Ω.

In the current work, fractional calculus has been used to solve ODEs from (1–8) [35]. The function can be approximated using any fractional derivatives defined by Miller and Ross, Grunwald-Letnikov, Riemann-Liouville, and M. Caputo. It is found that Caputo provides more accurate solutions for initial value problem (IVP) [7, 36] and is defined as

$$\frac{{d}^{\alpha }}{{d(x-a)}^{\alpha }}f=\frac{1}{\Gamma (n-\alpha )}{\int }_{a}^{t}\frac{{f}^{n}}{{(t-z)}^{\alpha +1-n}}dz$$
(9)

Here, n and α represent an integer and fractional order of derivative respectively. It has been assumed (n1) α < n.

Consider initial value problem (IVP).

$${D}^{\alpha }y(t)=f(t,y(t)) y(0)={y}_{0}$$
(10)

where: 0 < α ≤ 1, t ≥ 0. The function y(t) can be estimated using set of points (ti, y(ti)) which are generated by Caputo's method. The interval [0 T ] is split into k equal parts of width h = T/k each using nodes i for I = 0, 1, 2, ...k. where y(t), Dαy(t), and D2αy(t) are continuous within the interval [0 T ]. We expanded y(t) around t = t0 = 0 using the generalized Taylor series. For every t there is a constant value C1 such that

$$y({t}_{1})=y({t}_{0})+{D}^{\alpha }(y(t))({t}_{0})\frac{{h}^{\alpha }}{\Gamma (\alpha +1)}+ {D}^{2\alpha }y(t)({C}_{1})\frac{{h}^{2\alpha }}{\Gamma (2\alpha +1)}$$
(11)

Here, \(\mathrm{by replacing }{D}^{\alpha }(y(t))({t}_{0})=f({t}_{0},y({t}_{0},{y}_{0})\) into Eq. (11)

$$y({t}_{1})=y({t}_{0})+{D}^{\alpha }f({t}_{0}-y({t}_{0},{y}_{0}))({t}_{0})\frac{{h}^{\alpha }}{\Gamma (\alpha +1)}+ {D}^{2\alpha }y(t)({C}_{1})\frac{{h}^{2\alpha }}{\Gamma (2\alpha +1)}$$
(12)

If the step size h is chosen small enough, you can ignore the quadratic term in h2α and get

$$y({t}_{1})=y({t}_{0})+{D}^{\alpha }f({t}_{0}-y({t}_{0},{y}_{0}))({t}_{0})\frac{{h}^{\alpha }}{\Gamma (\alpha +1)}$$
(13)

Repeat the above derivation process to approximate the function. y(t). The Euler formula can be generalized as

$${t}_{i+1}={t}_{i+1}+1$$
(14)
$$y({t}_{i+1})=y({t}_{i})+\frac{{h}^{\alpha }}{\Gamma (\alpha +1)}f({t}_{i},y({t}_{i},{y}_{i})) \,i=\mathrm{0,1},2...k-1$$
(15)

Eqs. (1) to (8) is solved by using Eq. (15) as

$$\frac{{d}^{\alpha }S(t)}{dt}=-\frac{\beta (S\left(t\right)I\left(t\right)+q(A\left(t\right))}{N}-\Omega S(t)$$
(16)
$$\frac{{d}^{\alpha }E(t)}{dt}=\frac{\beta (S\left(t\right)I\left(t\right)+q(A\left(t\right))}{N}-\eta E\left(t\right)$$
(17)
$$\frac{{d}^{\alpha }I(t)}{dt}=\rho \eta E\left(t\right)-\gamma I(t)$$
(18)
$$\frac{{d}^{\alpha }A(t)}{dt}=(1-\rho )\eta E\left(t\right)-\gamma I(t)$$
(19)
$$\frac{{d}^{\alpha }Q(t)}{dt}=\gamma (I\left(t\right)+A\left(t\right)-\lambda \left(t\right)Q\left(t\right)-k\left(t\right)Q\left(t\right))$$
(20)
$$\frac{{d}^{\alpha }R(t)}{dt}=\lambda \left(t\right)Q(t)$$
(21)
$$\frac{{d}^{\alpha }D(t)}{dt}=k\left(t\right)Q(t)$$
(22)
$$\frac{{d}^{\alpha }T(t)}{dt}=\Omega S(t)$$
(23)

In the present work, Eqs. (16) to (23) have been solved using Capto’s fractional derivative.

Flow-chart of the proposed work in shown in the Fig. 2.

Fig. 2
figure 2

Flow-Chart of the proposed model

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3 Results

The Python language was used to implement the proposed mathematical model. Table 2 shows the hardware configuration of the machine used.

Indian COVID dataset were chosen to carry out validation of the of the proposed model [37]. Spread analysis of COVID using linear, quadratic, cubic and quartic polynomials is shown in Figs. 3 and 4.

Fig. 3
figure 3

COVID prediction using regression model

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Fig. 4
figure 4

COVID prediction using regression model

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Figures 3 and 4 show four different trend line plots showing the growth of COVID. As can be visually analyzed using Fig. 3a, when we try to fit a straight line to the growing cases, we find that the straight line does not grow steadily over time and the error increases. But we can see in Fig. 3b that if we increase the growth from linear to quadratic then an error is reduced. Hence, linear is not suitable in the case of COVID cases. But it can be visually analyzed from Fig. 3a and b that both linear and quadratic give more error and hence higher order is required for great fitting.

The growth of confirmed cases in recent times has been a major concern for many countries around the world. It has been observed that the growth of cases is not linear, which makes it difficult to predict the future trend. We analyzed the data using a second-order polynomial to find patterns in the COVID case increase. Analysis showed that the increase in the cases is still high even when compared to the quadratic equation. The quadratic equation has an R-squared value of 0.7814, which suggests that the data are still highly variable, and cannot be explained by the equation. In regression models, the coefficient of determination or R2 is a statistical measure that indicates % of variation in the dependent variable explained by independent variables. In this case, the dependent variable is confirmed case and the independent variable is time. The R2 value of 0.7814 indicates that approximately 78% of the variation in the increase in confirmed cases can be explained by a second-order polynomial. This suggests that there are other factors contributing to the increase in cases that are not captured in the equation. In Fig. 4a, a cubic polynomial has been applied and the trend line fit is fairly accurate. In Fig. 4b, a polynomial of degree 4 is applied and the trend line fit is more accurate than the fitted line using a polynomial of degree 3. We can conclude that before the lockdown, COVID cases increased by a polynomial of degree 4. The R2 is 0.97 which means that the polynomial of degree 4 explains variation in dependent with independent variable more accurately.

An analysis of the COVID spread after the lockdown from 25 March 2020 to 25 December 2020 was also analyzed. The results obtained are shown in Fig. 5. Here we draw various graphs to analyze the behavior of the infection rate after the initial lockdown. To analyze the behavior, three different trend lines are shown in the Figs. 5a–c. A linear fit does not meet the requirements, as can be easily analyzed visually using Fig. 5a. So the degree of the polynomial has increased to 2. In Fig. 5b, we can see that the accuracy is better compared to the degree 1 polynomial. In Fig. 5c, the degree of the polynomial is increased to 3, and we find that the trend line can be fitted more accurately. Therefore, it has been observed that the best-fitting curve is a third-order polynomial. The R-squared value is 0.8358, implying higher growth over time and reduced uncertainty after lockdowns were imposed.

Fig. 5
figure 5

COVID prediction after imposing lock-down in India

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Figure 6 shows a graph of the spread of COVID-19 in the second wave. It came into existence in India on July 13, 2021. In Figs. 6a–c, 1st and 2nd order polynomials are used to fit the trend lines. As can be seen from the figure. From Figs. 6a–c, Fig. 6a fits the trend line more accurately than the fitted lines shown in Figs. 6b, c. You can see that Fig. 7 shows the second wave trendline after the lockdown was imposed. Figures 7a–c show trend line fitting with polynomials of orders 1, 2, and 3. You can visually understand Fig. 7 a and b. It doesn't exactly fit the trend line. Therefore, a cubic polynomial fits the trend line better, as shown in Fig. 7c. A decrease in the number of cases has been observed over time. Data collected from June 24, 2021 onwards. You can clearly see the decrease in the COVID cases. Polynomial regression was used and the trend line was found to follow a polynomial of degree 3. The fitted straight line has an R-squared value of 0.98. The third wave of the new coronavirus began in India around December 28, 2021. Some people are affected by coronavirus even after being vaccinated. Figure 8 shows the daily number of confirmed cases at the start of the third wave of COVID-19. Figures 8a and b show trend line fitting using first- and second-order polynomials. Figure 8a visually shows that the trend line cannot be fitted accurately compared to fitting the trend line using a polynomial of degree 2. Therefore, we can see that the 2nd order polynomial is a better approximation to the trend line. The trend lines are shown in Figs. 9a and b. After the peak of the new coronavirus passed, the number of infected people began to decline. From Figs. 9a and b, we can visually see that the two degree 2 polynomials are more accurate in fitting the trend line compared to the degree 1 polynomial. Therefore, it was observed that the rate of decline is a quadratic function, the curve that best fits the regression line with an R-squared value of 0.97. Table 3 shows the R2 values for various case scenarios. Results obtained with the proposed fractional mathematical model are shown in Figs. 10 and 11.

Fig. 6
figure 6

COVID prediction in Second Wave in India

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Fig. 7
figure 7

COVID prediction in second wave after imposing lock-down

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Fig. 8
figure 8

COVID prediction in the third wave

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Fig. 9
figure 9

Fall down of COVID spread in the third wave in India

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Table 3 R2 value for different COVID prediction using different degrees of polynomials
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Fig. 10
figure 10

COVID prediction in the analysis by proposed fractional mathematical model

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Fig. 11
figure 11

COVID prediction in the analysis by proposed fractional mathematical model

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In Fig. 10a and b, results obtained for fractional order alpha=1 and alpha = 0.5 has been plotted respectively. In Fig. 11a and b, results obtained for fractional order alpha = 0.7 and alpha = 0.9 has been plotted respectively. As it can be easily analyzed that for different fractional orders, different results are obtained. Hence, a user has flexibility in choosing fractional order as per requirement and accuracy. In the model, alpha is arbitrary order of derivative that can be tuned to predict the corona spread more accurately.

4 Discussion

4.1 Theoretical Contributions

The current work is about to explore application of fractional calculus. Frac- tional calculus has been applied in many research fields such as science, engineering, medical and signal processing. It has been found that fractional calculus is more responsive as compared to integral one. So, in this manuscript, fractional calculus has been used to generalize integral ODE that is used to build mathematical model for early prediction of disease. It has been found the fractional calculus is highly responsive due to arbitrary order of derivative. The manuscript presented a mathematical model for early prediction of COVID disease. The proposed model has strong influence on society as the model predicts case in the timeline. Based on prediction, necessary counter measures can be made to prevent disease spread. The government can use these prediction data to prepare hospital facility, supplying sufficient medicines, and providing fooding and lodging facility to needy peoples. In this way, the model has great impact on the society. The proposed mathematical model is not only suitable to predict COVID cases but can be applied in other diseases where disease dynamics are not clear. In the proposed model, differential equations 16–30 have been applied to predict number of peoples in different compartments such as susceptible, exposed, infectious, asymptomatic, quarantined peoples, recovered peoples, death peoples and protected peoples. Differential equations have used to calculate change in number of peoples with respect to time. In the similar way, in the other diseases, these equations will give change in number of peoples with respect to time in that disease. In this way, we can predict number of cases in other diseases. The only requirement is to be tune different parameters listed in Table 2 according to that disease. The model per- forms well by setting accurate parameters which are obtained through study of the disease. Hence, estimating parameters in disease is only limitation of the presented model.

Regression is a machine learning technique employed to uncover the connection between independent and dependent variables. It has been utilized in analyzing the spread of COVID, accurately predicting the progression of the disease’s cases. This indicates that regression is effective for forecasting COVID growth. But this model cannot detect the peak point of the disease and also the deadline of the disease. Hence, mathematical modeling has been proposed in the present manuscript.

Mathematical models have shown good performance in predicting diseases with unclear dynamics, such as plague. This model uses ODEs to measure the number of cases. It has been observed that these models fail to predict cases due to the integer order of derivatives used in mathematical modeling. Fractional calculus gives you the flexibility to choose any order of derivation (non-integer) and increases your information processing power. Fractional calculus based mathematical model is designed to predict COVID cases. This model not only predicts the number of cases in advance, but also provides more accurate forecasts in terms of predicting the peak point and deadline of the disease.

4.2 Implications for Practice

The model presented in the manuscript has been validated on Indian COVID data. It has been found that the presented model not only predicts spread more accurately but also calculates the peak point of COVID cases and also the deadline for the disease.

The presented model is very useful in such cases where the disease nature is not clear in advance. The proposed model can be modified to incorporate new parameters for new diseases.

5 Conclusion

The mathematical model for early prediction of COVID disease is presented in the manuscript. Such model prediction is very useful since government takes necessary counter measures such distribution of medicines, preparation of hospital beds, oxygen supply based on early prediction of disease. By using such models, peoples can be saved from disease and mortality ratio can be minimized. In this work, people are divided into different compartments based on characteristics such as insensitive, vulnerable, infected, infected, asymptomatic, quarantined, recovered, and deceased. All compartments are parameter dependent. Changes in different compartments were analyzed using the fractional differentiation method. The proposed model is independent of disease dynamics. This depends on various parameters such as defense rate, infection rate, total population, reciprocal of mean incubation period, likelihood of symptomatic infection, isolation rate and recovery rate. and mortality. The values for these parameters are determined by research and vary from country to country. The proposed model is validated using Indian COVID data. The proposed model predicted the number of infected, infected, quarantined, dead, and recovered over time. We find that by modifying the parameters, the model can predict COVID-19 cases more accurately. You can change the parameters to predict cases in other countries. This study aimed to examine the application of regression models in the prediction of COVID-19. The study observed different scenarios before and after lockdowns were imposed in the first, second and third waves. Propagation scenarios turned out to be non-linear in all cases. Spread followed grade 2 and 3 non-linear trend lines, and regression models were used to predict COVID spread in each of these scenarios. Results showed that the model accurately predicted the spread of the virus in every case. Grade 2 and grade 3 non-linear trend lines were useful in identifying the viral spread pattern and predicting its behavior. This study highlights the importance of using regression models to predict the COVID spread. This approach will help policymakers make informed decisions about imposing lockdowns and other counter measures to curb the virus spread. By accurately predicting the spread of the virus, regression models can help prevent overwhelming health systems and reduce cases and deaths from COVID disease. In summary, this study presentists the effectiveness of using regression models in predicting the spread of COVID-19. The order 2 and order 3 nonlinear trendlines provide valuable insight into order. Analyze virus behavior and help identify patterns of virus spread. This information will help policy makers make informed decisions and take appropriate measures to curb the spread of the virus. We also know that given historical data, machine learning models can accurately predict disease. The proposed model is suitable not only for predicting COVID-19, but also for other diseases for which historical data are scarce and disease dynamics are unclear. In the future, other parameters such as vaccination coverage, public health interventions, personal behavior, social distancing, and wearing face signs could be added to monitor the impact of these parameters on the spread of COVID-19.