An Accurate Mathematical Epidemiological Model (SEQIJRDS) to Recommend Public Health Interventions Related to COVID-19 in Sri Lanka

COVID-19 has been causing negative impacts on various sectors in Sri Lanka as a result of the public health interventions that government had to implement in order to reduce the spreading of the disease. Equivalent work carried out in this context is outdated and close to ideal models. This research is carried out in a crucial time which the daily deaths are rapidly increasing which arise the requirement for an accurate and practical model to predict the mortality in order to take decisions regarding public health interventions. This paper presents a mathematical epidemiological model called SEQIJRDS to predict on COVID-19. The model has been validated for the COVID 19 pandemic in Sri Lanka. The results show that the model outstands many of the state-of-the-art SEIR epidemiological models such as Imperial, IHME once properly parameterized. At the end;this work recommends public health interventions at this crucial time to save people's lives based on the predictions of the proposed model. Specifically, 3 recommendations called minimal, sub-optimal and optimal recommendations are provided for public health interventions.

be considered as the most susceptible middle-income country due to the impact of COVID -19 [69]. 48 However, the clear analysis about rapid change of LKR and impact of GDP value to the economy of 49 Sri Lanka is lacking in the research field. The economic impact to Sri Lanka is well described in [1] but 50 it presents mainly the impact in 2019 to early 2020 period. When making public health interventions 51 and preparing policies; a compromise has to be made between the economy and public health as the 52 economic impact due to COVID19 preventative measures can drastically effect on the economy in 53 South Asia which Sri Lanka is a member [24]. 54 Secondary and higher education 55 Higher education in Sri Lanka is another major impacted area because of COVID -19. Universities 56 encounter several challenges in terms of online delivery, problems of practical test via online mode, 57 assessments, examinations and supervision of the thesis. Survey done in the South Eastern University 58 Sri Lanka shows that 59% were interested in pursuing higher education online but later they lost hope 59 in it because of poor connections, lack of devices, power outages and so on [69]. But schools and 60 universities with advanced facilities have been able to carry out virtual classes. Online education is a 61 new method in Sri Lankan education and it is not familiar for Sri Lankan students and teachers so that 62 there are technology challenges and there is a tendency for increment of the mental stress of students 63 and teachers [70]. 64 Tourism However, a cross country study of initial growth rate of COVID19 impacted by spreading factors 122 such as non-pharmaceutical interventions, demography, society and climate have been performed 123 in [14]. But in this paper, additional spreading factors are taken into consideration and an updated 124 review is presented specifically for Sri Lanka. The paper in [15] discusses the effectiveness of different 125 lock down policies globally and derives the mobility changes based on them. This paper will discuss 126 the how relevant is such a model to Sri Lanka. 127 At the moment, Sri Lanka is in the middle of a collapse in most sectors of the country. People have 128 been suffering from this pandemic for nearly two years. Therefore, this research is also an attempt to 129 recommend potential interventions to prevent COVID19 deaths will occur in coming months to Sri     The data was collected into a Microsoft Excel Spreadsheet file. No automation tool was used for 148 importing the data into the Excel sheet. Raw Data from the reports were manually inserted.  We minimize the bias that occurs from data of different sample sizes collected from different 155 sources for analysis as a data pre-processing procedure. For example; we model the parameter mobility 156 (µ) as a normalized parameter in our design which will be explained later.   • P S P S P S is the probability of developing full immunity by vaccination 213 • P I P I P I is the probability of recovering with full immunity from non-hospitalized infectants 214 • P J P J P J is the probability of recovering with full immunity from hospitalized infectants 215 Differential equations can be written as follows by considering the rate of change of population at 216 each of the compartments.

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Initially at time t = 0 (just before the disease is going to infect for the first time for already exposed  We solve the system of First order differential equations using MATLAB software tool. The 231 statistical analysis of the historical data was performed using Microsoft Excel to deduce the rates and 232 probabilities.

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Each of the variables can be modelled as given in the following subsections. The quarantine rate is an important parameter which can control the spreading of the disease. But 247 the problem is that there is no data to obtain this mainly because there has been double counting (Not Table 1. Summary table of  252 where gamma 0 is the base quarantine rate. We obtained the value for gamm 0 by curve fitting for 253 the historical data since the data is erroneous. can be summarized as in Table 1 which dates obtained from [43-48].

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The mobility of Sri Lankans during the pandemic period is shown in Figure 2. Here, data was In Figure 2, it can be observed a low cross correlation between all non-residential data and 260 residential data showing that travel restrictions have effectively reduced non-residential mobility but, has increased residential mobility. However, as residential groups have very small size groups 262 typically 2-4 people, the impact on spreading the disease is low from residential groups. 263 So, to observe the mobility; we calculate the average mobility across 6 different sections given in 264 Figure 2 and use min-max normalization to map into a variable between 0 to 1. The result is as seen in  Sri Lanka. Figure 4 shows the cumulative vaccination values at the end of each month. Hindu new year vacation period. 291 Figure 5 shows the variation of average vaccination per of each month for each type of the vaccine.

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As seen from Figure 5, the Astrazenaca vaccinate has been mainly given at the start of the given in Figure 6 299 η should be found graphically using the graph in Figure 6 which has a non-linear variation. This 300 η values will be used in solving the differential equations in the proposed SEQIJRDS model.   will go only to the removed class R. So, the real daily recovered patients with 100% immunity 319 against the disease will be different to the one reported. But we can approximate α 2 using the 320 (discharged p atients/number i n w ard) ratio as plotted in Figure 9. It should be noted that the fraction of COVID19 victims who recover without being diagnosed as 322 infectants is not reported and hence unknown. So, the value of α 1 has to be learned using curve fitting 323 for historical data. From data, we calculate the ratio between the number of deaths and infected patients for 326 hospitalized population as shown in Figure 10. The value at each point of the graph will be used as 327 initial conditions when solving the system of differential equations. will not be reported as COVID 19 death. In this paper we set (α 3 = α 4 ) which is a fair assumption since 330 both non-isolated infectants and isolated infectants are evolved from the same exposed population.  Figure 11 shows the under-reporting adjusted variation of the death class at the end of each month 340 during the pandemic.   Here, it should be noted that learned parameters up to the Month of June will be used in generating 361 the predictions. The parameters learned in July and August are not used as they are generated as 362 predictions.
where A t Absolute value of the Prediction P t at time t. n is the number of predicted values. Figure   364 13 shows the proposed model's predictions for the mortality due to COVID 19 and actual mortality 365 which occurred. Here, it should be noted that as mentioned before; 50% under-reporting situation is 366 considered. As proved graphically in Figure 13; MAPE is low for the first 4 weeks and gradually increases 368 there onwards which agrees with the typical behavior of forecasting models. compare the proposed model's performance Vs. IHME for future predictions as shown in the Figure   382 14.
383 Figure 14. Comparison of daily death prediction of the proposed model and IHME model As an effect measure; we compute the standardized mean difference between predictions of the 384 two models. We use the Equation 12 to compute the mean difference.

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Standardized Mean Di f f erence = M 1 − M 2 SD pooled (12) The SMD between the two predictions is 0.25 indicating there is only a small difference between 386 the prediction values of the two models.      We will now compare the parameter daily deaths for above 3 recommendations against the worst 466 case of continuing existing quarantine only to obtain the following result shown in Figure 19 467 It is evident from Figure 19  and optimal solution not only will be able to reduce number of deaths; but also, they have successfully 473 prevented further spreading of the disease by the beginning of December. As seen from the results  As it was mentioned separately in detail in the methodology section, we summarize the assumed 484 or derived/learned parameters for the model due to lack of data as shown in Table 4. 485 Table 4. Based on non-availability of exact population in districts and non-availability of COVID19 data and 499 mobility data divided across districts; we refrain from modeling in this procedure.