# Prediction of Epidemic Peak and Infected Cases for COVID-19 Disease in Malaysia, 2020

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{2}) of 0.9964. The results also show that an intervention has a great effect on delaying the epidemic peak and a longer intervention period would reduce the epidemic size at the peak. The study provides important information for public health providers and the government to control the COVID-19 epidemic.

## 1. Introduction

## 2. Methods

#### 2.1. SEIR Model for Peak Prediction

dE(t)/d(t) = βS(t)I(t) − αE(t),

dI(t)/d(t) = αE(t) − γI(t) − MI(t),

dR(t)/d(t) = γI(t),

dD(t)/d(t) = MI(t)

^{−-1}) and infectious (γ

^{−1}) periods are 5 days and 10 days, respectively. Thus, the α and γ values are 0.2 and 0.1, respectively. The total number of deaths and confirmed cases up to 5 April are 61 and 3662, respectively, and thus the mortality rate M is 0.016 (61/3662). We fixed the unit time to be 1 day and S + E + I + R + D = 1, such that each population implies the proportion to the total population. Let assume that there is one infected case recorded at time t = 0 among the Malaysian population of N = 32.6 × 10

^{6}[26]; that is, X(0) = pNI(0) = 1, where

^{6}). The block diagram of the SEIR model is attached in Appendix A as Figure A1. It is assumed that there are no exposed, recovered, and death cases at t = 0, and hence,

_{0}represents the expected number of secondary cases resulted from an infected individual [29]. It is calculated as the leading eigenvalue of the next generation matrix G = FV

^{−1}[30], where

_{0}is negligible as the population number (N) is 32.2 × 10

^{6}. The coefficient parameters of the SEIR model are summarized in Table 1. Note that the estimation of β and $\mathcal{R}$

_{0}values are presented in the next subsection.

#### 2.2. β. Estimation Using GA

^{″}) is defined as in Equation (8).

_{0.2 ≤ β ≤ 0.4}C(β),

- Population initialization: In order to find a solution to the problem of the cost function, the GA initially creates a number of populations that randomly encodes the chromosomes (individuals). Then, the cost values of the generated population are evaluated.
- Selection: In this process, each individual identified by its associated cost is ranked and the corresponding individual fitness is selected. According to fitness, the best chromosomes from the population are then selected such that better fitness has a bigger chance to be selected. Subsequently, the solutions selected from one population are implemented to form a new population. This process is motivated by the new population potentially being better than the previous one. The selection process is performed using a certain function that fixes the generation gap. The selected individuals are then recombined.
- Crossover: To make new offspring (children) for the following iteration, the selected individuals (parents) have to undergo a crossover with a crossover probability. However, if there is no crossover performed, the offspring is an exact copy of the parents.
- Mutation: In this process, the information in the chromosomes is randomly modified. The genes occasionally mutate to be converted to novel genes. Based on mutation, it is possible to control the multifariousness of the population as well as to enhance the search capacity of the search scheme.
- Evaluation: For each individual, the cost function of the optimization problem is calculated. The stopping criterion of the GA is the number of iterations after which the process is stopped. For each iteration, the β value that has the minimum cost function is recorded. The distribution of the β values is then approximated by a normal distribution with a mean and standard deviation.

#### 2.3. ANFIS for Short-Term Forecasting

_{1}then y

_{1}= P

_{1}x + r

_{1},

_{2}then y

_{2}= P

_{2}x + r

_{2}.

_{i}= μ

_{Ai}(x), where μ (x) is MF.

_{i}represents the weight strength of one rule.

_{i}= μ (x)

_{i}μ (x)

_{i+}

_{1}and i = 1,2.

^{®}Software (MathWorks Inc.) is used to implement the ANFIS parameters that are summarized in Table 3. In this study, as the number of infected cases is nonlinearly changed from day to day, the ANFIS model is used. The ANFIS model forecasts the numbers of infected cases for the upcoming 5 days based on the numbers of infected cases for the last 10 days. The dataset of 10 days is divided into training (70%) and testing (30%) datasets which are implemented in the ANFIS model. After that, the trained ANFIS model is used to forecast the numbers of cases for the next 5 days. The input and output variables are day number and number of infected cases, respectively.

^{2}) were used as follows [38,39]:

## 3. Results

#### 3.1. Infection Rate (β) Estimation

^{−9}at the iteration number 819, which indicates that there is no better cost value than 1.098 × 10

^{−9}based on GA. The optimum β values obtained for the entire population size of 200 is shown in Figure 5. The β values are approximated by the normal distribution and, subsequently, the infection rate β is 0.228 ± 0.013. Based on Equation (5), the basic reproductive number is 2.28 ± 0.13 as γ = 0.1.

#### 3.2. Epedimic Peak Prediction

_{max}) = max

_{0 < t < 365}X(t). Based on the current report, the p is around 0.084. Subsequently, Figure 6 shows a one-year behavior of X(t) for the determined infection rate β = 0.228 ± 0.013.

_{0}, it is clear that the epidemic peak and size are responsive to the identification rate p. Furthermore, a lower identification rate leads to a lower number of infected cases, such that the number of infected cases decreases from 2.582 × 10

^{5}to 3.077 × 10

^{4}at the epidemic peak with p = 0.01.

#### 3.3. Epidemic Peak after Possible Interventions

_{new}= 0.17) during the period from 05 April (t = 72) to the desired day (t = T > 72), and we fix p to 0.084 in what follows. Firstly, it is assumed that the intervention is adopted for 2 months; that its, T is equal to 134 (72 + 62). In this situation, the epidemic peak t

_{max}is shifted 30 days later from 26 July to 26 August. It is clear that the epidemic size remains relatively unchanged. On the other hand, if the interventions are adopted for three months from 05 April to 04 July (T = 72 + 92 = 164), then the epidemic peak t

_{max}is moved back from 26 July to 09 September. It can be observed that the epidemic size is significantly reduced. Figure 8 shows the real-time prediction of infected cases that are identified between t = 0 and t = 365 for no intervention, two months intervention, and three months intervention.

_{max}is linearly delayed as the intervention period increases from 72 ≤ T ≤ 263 and then fixed to t

_{max}for T > 263.

_{max}). It is observed that the number of infected cases is monotonically declined and fixed as T increases. Interestingly, the change in the number of infected cases is rapidly increased for T > 72. This implies that an early intervention over a relatively small duration can be effective to reduce the epidemic size and flatten the curve.

#### 3.4. Short-Term Forecasting

^{2}obtained while training the ANFIS model using the training and testing datasets.

^{2}values are 96.8, 0.041, 2.45%, and 0.9964, respectively. These results indicate a very low RMSE, NRMSE, and MAPE, but a high R

^{2}.

## 4. Discussion

_{0}is 2.28 ± 0.13. This value is relatively close to the estimated value by the World Health Organization (WHO), which ranges from 2 to 2.5 for COVID-19 [40]. In addition, this value is not so different from recent estimations: 2.24–3.58 [41], 2.0–3.1 [42], and 2.06–2.52 [43] for COVID-19. However, some studies reported higher $\mathcal{R}$

_{0}values of 3.28, 2.90, and 3.11, as reported in [44,45,46], respectively. This bias in estimating the $\mathcal{R}$

_{0}value is probably attributed to limited available data over a short period and also highly depends on the settings. Furthermore, the estimation of $\mathcal{R}$

_{0}strongly relies on the estimation method and the validity of the assumptions for some coefficients. Thus, the availability of more data over a long period would provide a more accurate estimation and form a clearer trend.

- The number of people who had contact with COVID-19 patients is enormous, as reported in [48]. This could make the process of tracking and isolating more complex. Based on the information reported by Chinese medical doctors involved in Wuhan, the critical cases form 10% of the total number of infected people. The early diagnosis and treatment would reduce the flow of COVID-19 patients into the ICU unit [49].
- Poor experience in treating and managing cases with different levels of infection. For instance, severe cases should be kept under monitoring with intensive care, while mild cases without clear symptoms should be kept with less intensive care in the hospitals. However, patients under investigation should be placed in special isolation outside the hospitals. This kind of management would ease the treating process with the currently available equipment [50].
- The current MCO implemented in Malaysia is limited to aiding the awareness of the people to the danger of COVID-19. For the first 10 days of the MCO, 60% of the public has obeyed the MCO issued by the government [51]. Thus, more restrictions are needed to enforce the MCO. By increasing the public awareness, the infection rate will be reduced, which would result in decreasing the reproductive number and delaying the epidemic peak.

^{2}= 0.9964), which is very close to the perfect value of 1; (2) a low NRMSE value (NRMSE = 0.041), which is highly close to the perfect values of 0; and (3) a high MAPE value (MAPE = 2.45%), which is less than 10% [52]. The main motivation behind using the ANFIS model instead of parametric models (e.g., likelihood and Bayesian methods) is that ANFIS is able to achieve a high accuracy using only a few datasets and is easy to be deployed, such that the ANFIS model uses one input as day number, while parametric models require at least four inputs as well as estimation of the coefficients.

_{0}. Lastly, the ANFIS model is applicable for short-term forecasting, and so it cannot be used to predict the epidemic peak of COVID-19 as the ANFIS model does not consider the recovered and death rates.

## 5. Conclusions

^{2}values are 0.041, 2.45%, and 0.9964, respectively.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Data availability

^{®}codes used to generate the results are available from the corresponding author upon request.

## Appendix A

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**Figure 6.**Real-time variation in the number of infected cases identified at time t for p = 0.084 and β = 0.215, β = 0.228, and β = 0.241. The text arrows represent the t

_{max}for each infection rate.

**Figure 7.**Real-time variation in the number of infected cases identified at time t for p = 0.01 and β = 0.215, β = 0.228, and β = 0.241. The text arrows represent the t

_{max}for each infection rate.

**Figure 8.**Real-time variation in the number of infected cases (0 ≤ t ≤ 365) for p = 0.084. The red dotted lines represent the epidemic peak.

**Figure 9.**The relationship between the desired day for intervention T and (

**a**) the epidemic peak t

_{max}; (

**b**) the number of infected cases at epidemic peak t

_{max}.

**Figure 11.**Estimated and actual infected cases using the (

**a**) training dataset and (

**b**) testing dataset.

Coefficient | Description | Value |
---|---|---|

α | Onset rate | 0.2 |

γ | Removal rate | 0.1 |

M | Mortality rate | 0.016 |

N | Malaysia population | 32.6 × 10^{6} |

p | Identification rate | 0.084 |

Parameter | Value | Parameter | Value |
---|---|---|---|

Population size | 200 | Mutation rate | 0.02 |

Number of iterations | 1000 | Mutation percentage | 0.9 |

Crossover percentage | 0.95 |

Parameter | Method/Value | Parameter | Method/Value |
---|---|---|---|

Fuzzy structure | Sugeno-type | No. of epochs | 300 |

Rules clustering | Grid partition | Input | Day number |

MF type | Gaussian | Output | Infected cases |

Optimization method | Hybrid | Output MF | constant |

Parameter | Training Data | Testing Dataset |
---|---|---|

RMSE | 18.53 | 46.87 |

NRMSE | 0.012 | 0.032 |

MAPE | 1.31% | 2.79% |

R^{2} | 0.9973 | 0.9998 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Alsayed, A.; Sadir, H.; Kamil, R.; Sari, H.
Prediction of Epidemic Peak and Infected Cases for COVID-19 Disease in Malaysia, 2020. *Int. J. Environ. Res. Public Health* **2020**, *17*, 4076.
https://doi.org/10.3390/ijerph17114076

**AMA Style**

Alsayed A, Sadir H, Kamil R, Sari H.
Prediction of Epidemic Peak and Infected Cases for COVID-19 Disease in Malaysia, 2020. *International Journal of Environmental Research and Public Health*. 2020; 17(11):4076.
https://doi.org/10.3390/ijerph17114076

**Chicago/Turabian Style**

Alsayed, Abdallah, Hayder Sadir, Raja Kamil, and Hasan Sari.
2020. "Prediction of Epidemic Peak and Infected Cases for COVID-19 Disease in Malaysia, 2020" *International Journal of Environmental Research and Public Health* 17, no. 11: 4076.
https://doi.org/10.3390/ijerph17114076