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In this paper, an epidemic compartmental model with saturated type treatment function is presented to investigate the transmission dynamics of COVID-19 with a case study of Spain (in Europe). We obtain the basic reproduction number of the model which plays a very important role in disease spreading. We show that if the basic reproduction number is less than unity then the disease-free equilibrium point is locally asymptotically stable, but making the basic reproduction number less than unity is not sufficient to eradicate COVID-19 infection which is shown through backward bifurcation. The model is validated with the real COVID-19 data of Spain (in Europe), Algeria (in Africa), and India (in Asia) and also estimated important model parameters in all cases. The effect of an important model parameter for controlling the disease spreading is also investigated for the infection scenario of Spain only. We establish that the asymptomatic class plays a very important role for spreading this pandemic disease. The effective reproduction number has been estimated which varies in time in Spain. Finally, the model is reformulated as an optimal control problem which shows that the social distancing due to adapting a partial lockdown by some countries is highly effective for controlling COVID-19.
ABSTRACT
BACKGROUND: Response to the unprecedented coronavirus disease 2019 (COVID-19) outbreak needs to be augmented in Texas, United States, where the first 5 cases were reported on March 6, 2020, and were rapidly followed by an exponential rise within the next few weeks. This study aimed to determine the ongoing trend and upcoming infection status of COVID-19 in county levels of Texas. METHODS: Data were extracted from the following sources: published literature, surveillance, unpublished reports, and websites of Texas Department of State Health Services (DSHS), Natality report of Texas, and WHO Coronavirus Disease (COVID-19) Dashboard. The 4-compartment Susceptible-Exposed-Infectious-Removal (SEIR) mathematical model was used to estimate the current trend and future prediction of basic reproduction number and infection cases in Texas. Because the basic reproduction number is not sufficient to predict the outbreak, we applied the Continuous-Time Markov Chain (CTMC) model to calculate the probability of the COVID-19 outbreak. RESULTS: The estimated mean basic reproduction number of COVID-19 in Texas is predicted to be 2.65 by January 31, 2021. Our model indicated that the third wave might occur at the beginning of May 2021, which will peak at the end of June 2021. This prediction may come true if the current spreading situation/level persists, i.e., no clinically effective vaccine is available, or this vaccination program fails for some reason in this area. CONCLUSION: Our analysis indicates an alarming ongoing and upcoming infection rate of COVID-19 at county levels in Texas, thereby emphasizing the promotion of more coordinated and disciplined actions by policy-makers and the population to contain its devastating impact.
ABSTRACT
COVID-19 takes a gigantic form worldwide in a short time from December, 2019. For this reason, World Health Organization (WHO) declared COVID-19 as a pandemic outbreak. In the early days when this outbreak began, the coronavirus spread rapidly in the community due to a lack of knowledge about the virus and the unavailability of medical facilities. Therefore it becomes a significant challenge to control the influence of the disease outbreak. In this situation, mathematical models are an important tool to employ an effective strategy in order to fight against this pandemic. To study the disease dynamics and their influence among the people, we propose a deterministic mathematical model for the COVID-19 outbreak and validate the model with real data of Italy from 15th Feb 2020 to 14th July 2020. We establish the positivity and boundedness of solutions, local stability of equilibria to examine its epidemiological relevance. Sensitivity analysis has been performed to identify the highly influential parameters which have the most impact on basic reproduction number (R0). We estimate the basic reproduction number (R0) from available data in Italy and also study effective reproduction numbers based on reported data per day from 15th Feb 2020 to 14th July 2020 in Italy. Finally, the disease control policy has been summarized in the conclusion section.
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BACKGROUND: Besides maintaining health precautions, vaccination has been the only prevention from SARS-CoV-2, though no clinically proved 100% effective vaccine has been developed till date. At this stage, to withhold the debris of this pandemic-experts need to know the impact of the vaccine efficacy rates, the threshold level of vaccine effectiveness and how long this pandemic may extent with vaccines that have different efficacy rates. In this article, a mathematical model study has been done on the importance of vaccination and vaccine efficiency rate during an ongoing pandemic. METHODS: We simulated a five compartment mathematical model to analyze the pandemic scenario in both California, and whole U.S. We considered four vaccines, Pfizer (95%), Moderna (94%), AstraZeneca (79%), and Johnson & Johnson (72%), which are being used rigorously to control the SARS-CoV-2 pandemic, in addition with two special cases: a vaccine with 100% efficacy rate and no vaccine under use. SARS-CoV-2 related data of California, and U.S. were used in this study. FINDINGS: Both the infection and death rates are very high in California. Our model suggests that the pandemic situation in California will be under control in the last quartile of the year 2023 if vaccination program is continued with the Pfizer vaccine. During this time, six waves may happen from the beginning of the immunization where the case fatality and recovery rates will be 1.697% and 98.30%, respectively. However, according to the considered model, this period might be extended to the mid of 2024 when vaccines with lower efficacy rates are used. On the other hand, the daily cases and deaths in the U.S. will be under control at the end of 2026 with multiple waves. Although the number of susceptible people will fall down to none in the beginning of 2027, there is less chance to stop the vaccination program if vaccinated with a vaccine other than a 100% effective vaccine or Pfizer, and at that case vaccination program must run till the mid of 2028. According to this study, the unconfirmed-infectious and infected cases will be under control at the end of 2027 and at the mid of 2028, respectively. INTERPRETATION: The more effective a vaccine is, the less people suffer from this malign infection. Vaccines which are less than 90% effective do not have notable contribution to control the pandemic besides hard immunity. Furthermore, specific groups of people are getting prioritized initially, mass vaccination and quick responses are required to control the spread of this disease.
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Background: Bangladesh hosts more than 800,000 Rohingya refugees from Myanmar. The low health immunity, lifestyle, access to good healthcare services, and social-security cause this population to be at risk of far more direct effects of COVID-19 than the host population. Therefore, evidence-based forecasting of the COVID-19 burden is vital in this regard. In this study, we aimed to forecast the COVID-19 obligation among the Rohingya refugees of Bangladesh to keep up with the disease outbreak's pace, health needs, and disaster preparedness. Methodology and Findings: To estimate the possible consequences of COVID-19 in the Rohingya camps of Bangladesh, we used a modified Susceptible-Exposed-Infectious-Recovered (SEIR) transmission model. All of the values of different parameters used in this model were from the Bangladesh Government's database and the relevant emerging literature. We addressed two different scenarios, i.e., the best-fitting model and the good-fitting model with unique consequences of COVID-19. Our best fitting model suggests that there will be reasonable control over the transmission of the COVID-19 disease. At the end of December 2020, there will be only 169 confirmed COVID-19 cases in the Rohingya refugee camps. The average basic reproduction number (R0) has been estimated to be 0.7563. Conclusions: Our analysis suggests that, due to the extensive precautions from the Bangladesh government and other humanitarian organizations, the coronavirus disease will be under control if the maintenance continues like this. However, detailed and pragmatic preparedness should be adopted for the worst scenario.