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Register a new userAnalysis and Prediction of COVID-19 Pandemic in Pakistan using Time-dependent SIR Model
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The current outbreak is known as Coronavirus Disease or COVID-19 caused by the virus SAR-COV-2 which continues to wreak havoc across the globe. The World Health Organization (WHO) has declared the outbreak a Public Health Emergency of International Concern. In Pakistan, the spread of the virus is on the rise with the number of infected people and causalities rapidly increasing. In the absence of proper vaccination and treatment, to reduce the number of infections and casualties, the only option so far is to educate people regarding preventive measures and to enforce countrywide lock-down. Any strategy about the preventive measures needs to be based upon detailed analysis of the COVID-19 outbreak and accurate scientific predictions. In this paper, we conduct mathematical and numerical analysis to come up with reliable and accurate predictions of the outbreak in Pakistan. The time-dependent Susceptible-Infected-Recovered (SIR) model is used to fit the data and provide future predictions. The turning point of the peak of the pandemic is defined as the day when the transmission rate becomes less than the recovering rate. We have predicted that the outbreak will reach its maximum peak occurring from late May to 9 June with unrecovered number of Infectives in the range 20000-47000 and the cumulative number of infected cases in the range of 57500-153100. The number of Infectives will remain at the lower end in the lock-down scenario but can rapidly double or triple if the spread of the epidemic is not curtailed and localized. The uncertainty on single day projection in our analysis after April 15 is found to be within 5%.
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Several analytical models have been used in this work to describe the evolution of death cases arising from coronavirus (COVID-19). The Death or `D model is a simplified version of the SIR (susceptible-infected-recovered) model, which assumes no recovery over time, and allows for the transmission-dynamics equations to be solved analytically. The D-model can be extended to describe various focuses of infection, which may account for the original pandemic (D1), the lockdown (D2) and other effects (Dn). The evolution of the COVID-19 pandemic in several countries (China, Spain, Italy, France, UK, Iran, USA and Germany) shows a similar behavior in concord with the D-model trend, characterized by a rapid increase of death cases followed by a slow decline, which are affected by the earliness and efficiency of the lockdown effect. These results are in agreement with more accurate calculations using the extended SIR model with a parametrized solution and more sophisticated Monte Carlo grid simulations, which predict similar trends and indicate a common evolution of the pandemic with universal parameters.
COVID-19 pandemic represents an unprecedented global health crisis in the last 100 years. Its economic, social and health impact continues to grow and is likely to end up as one of the worst global disasters since the 1918 pandemic and the World Wars. Mathematical models have played an important role in the ongoing crisis; they have been used to inform public policies and have been instrumental in many of the social distancing measures that were instituted worldwide. In this article we review some of the important mathematical models used to support the ongoing planning and response efforts. These models differ in their use, their mathematical form and their scope.
We studied the COVID-19 pandemic evolution in selected African countries. For each country considered, we modeled simultaneously the data of the active, recovered and death cases. In this study, we used a year of data since the first cases were reported. We estimated the time-dependent basic reproduction numbers, $R_0$, and the fractions of infected but unaffected populations, to offer insights into containment and vaccine strategies in African countries. We found that $R_0leq 4$ at the start of the pandemic but has since fallen to $R_0 sim 1$. The unaffected fractions of the populations studied vary between $1-10$% of the recovered cases.
OBJECTIVES: to describe the first wave of the COVID-19 pandemic with a focus on undetected cases and to evaluate different post-lockdown scenarios. DESIGN: the study introduces a SEIR compartmental model, taking into account the region-specific fraction of undetected cases, the effects of mobility restrictions, and the personal protective measures adopted, such as wearing a mask and washing hands frequently. SETTING AND PARTICIPANTS: the model is experimentally validated with data of all the Italian regions, some European countries, and the US. MAIN OUTCOME MEASURES: the accuracy of the model results is measured through the mean absolute percentage error (MAPE) and Lewis criteria; fitting parameters are in good agreement with previous literature. RESULTS: the epidemic curves for different countries and the amount of undetected and asymptomatic cases are estimated, which are likely to represent the main source of infections in the near future. The model is applied to the Hubei case study, which is the first place to relax mobility restrictions. Results show different possible scenarios. Mobility and the adoption of personal protective measures greatly influence the dynamics of the infection, determining either a huge and rapid secondary epidemic peak or a more delayed and manageable one. CONCLUSIONS: mathematical models can provide useful insights for healthcare decision makers to determine the best strategy in case of future outbreaks.
In this study, we present a new epidemiological model, with contamination from confirmed and unreported. We also compute equilibria and study their stability without intervention strategies. Optimal control theory has proven to be a successful tool in understanding ways to curtail the spread of infectious diseases by devising the optimal disease intervention strategies. We investigate the impact of distancing, case finding, and case holding controls while at the same time, we minimize the number of infected and dead individuals. The method consists of minimizing the cost functional related to infectious, death, and controls through some strategies to reduce the spread of the COVID19 epidemic.
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