STUDY OF INTEGER AND FRACTIONAL ORDER COVID-19 MATHEMATICAL MODEL

In this paper, we study a nonlinear mathematical model which addresses the transmission dynamics of COVID-19. The considered model consists of susceptible (S), exposed (E), infected (I), and recovered (R) individuals. For simplicity, the model is abbreviated as SEIR. Immigration rates of two kinds are involved in susceptible and infected individuals. First of all, the model is formulated. Then via classical analysis, we investigate its local and global stability by using the Jacobian matrix and Lyapunov function method. Further, the fundamental reproduction number ℛ0 is computed for the said model. Then, we simulate the model through the Runge–Kutta method of order two abbreviated as RK2. Finally, we switch over to the fractional order model and investigate its numerical simulations corresponding to different fractional orders by using the fractional order version of the aforementioned numerical method. Finally, graphical presentations are given for the approximate solution of various compartments of the proposed model. Also, a comparison with real data has been shown. [ FROM AUTHOR] Copyright of Fractals is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Mathematical modeling the dynamics of SARS-CoV-2 infection with antibody-dependent enhancement.

The advent and swift global spread of the novel coronavirus (COVID-19) transmitted by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have caused massive deaths and economic devastation worldwide. Antibody-dependent enhancement (ADE) is a common phenomenon in virology that directly affects the effectiveness of the vaccine, and there is no fully effective vaccine for diseases. In order to study the potential role of ADE on SARS-CoV-2 infection, we establish the SARS-CoV-2 infection dynamics model with ADE. The basic reproduction number is computed. We prove that when R 0 < 1 , the infection-free equilibrium is globally asymptotically stable, and the system is uniformly persistent when R 0 > 1 . We carry out the sensitivity analysis by the partial rank correlation coefficients and the extended version of the Fourier amplitude sensitivity test. Numerical simulations are implemented to illustrate the theoretical results. The potential impact of ADE on SARS-CoV-2 infection is also assessed. Our results show that ADE may accelerate SARS-CoV-2 infection. Furthermore, our findings suggest that increasing antibody titers can have the ability to control SARS-CoV-2 infection with ADE, but enhancing the neutralizing power of antibodies may be ineffective to control SARS-CoV-2 infection with ADE. Our study presumably contributes to a better understanding of the dynamics of SARS-CoV-2 infection with ADE.

Assessing the effectiveness of the intervention measures of COVID-19 in China based on dynamical method.

Normalized interventions were implemented in different cities in China to contain the outbreak of COVID-19 before December 2022. However, the differences in the intensity and timeliness of the implementations lead to differences in final size of the infections. Taking the outbreak of COVID-19 in three representative cities Xi'an, Zhengzhou and Yuzhou in January 2022, as examples, we develop a compartmental model to describe the spread of novel coronavirus and implementation of interventions to assess concretely the effectiveness of Chinese interventions and explore their impact on epidemic patterns. After applying reported human confirmed cases to verify the rationality of the model, we apply the model to speculate transmission trend and length of concealed period at the initial spread phase of the epidemic (they are estimated as 10.5, 7.8, 8.2 days, respectively), to estimate the range of basic reproduction number (2.9, 0.7, 1.6), and to define two indexes (transmission rate v t and controlled rate v c ) to evaluate the overall effect of the interventions. It is shown that for Zhengzhou, v c is always more than v t with regular interventions, and Xi'an take 8 days to achieve v c  > v t twice as long as Yuzhou, which can interpret the fact that the epidemic situation in Xi'an was more severe. By carrying out parameter values, it is concluded that in the early stage, strengthening the precision of close contact tracking and frequency of large-scale nucleic acid testing of non-quarantined population are the most effective on controlling the outbreaks and reducing final size. And, if the close contact tracking strategy is sufficiently implemented, at the late stage large-scale nucleic acid testing of non-quarantined population is not essential.

Threshold dynamics of a stochastic SIHR epidemic model of COVID-19 with general population-size dependent contact rate.

In this paper, we propose a stochastic SIHR epidemic model of COVID-19. A basic reproduction number $ R_{0}^{s} $ is defined to determine the extinction or persistence of the disease. If $ R_{0}^{s} < 1 $, the disease will be extinct. If $ R_{0}^{s} > 1 $, the disease will be strongly stochastically permanent. Based on realistic parameters of COVID-19, we numerically analyze the effect of key parameters such as transmission rate, confirmation rate and noise intensity on the dynamics of disease transmission and obtain sensitivity indices of some parameters on $ R_{0}^{s} $ by sensitivity analysis. It is found that: 1) The threshold level of deterministic model is overestimated in case of neglecting the effect of environmental noise; 2) The decrease of transmission rate and the increase of confirmed rate are beneficial to control the spread of COVID-19. Moreover, our sensitivity analysis indicates that the parameters $ \beta $, $ \sigma $ and $ \delta $ have significantly effects on $ R_0/ $.

Did the COVID-19 Lockdown in India Succeed? A Mathematical Study

In this study, we estimate the basic reproduction number (R0 ) for the ongoing COVID-19 pandemic for 10 seriously affected states and for the whole country for the lockdown period. For this, we formulate a SEIQHR mathematical model and fitted it to cumulative COVID-19 cases. The Government of India implemented the first phase of nationwide lockdown from March 25, 2020 to April 14, 2020 and extended the same from April 15, 2020 to May 3, 2020. We measure the effectiveness of the nationwide lockdown on the spread of COVID-19 in India. For this, we have estimated the basic reproduction number for three phases;namely March 14–31, 2020 (Phase I), April 1–15, 2020 (Phase II), and April 16–30, 2020 (Phase III). Our study finds that, in all the cases, the value of the R0 is minimum at the end of phase III. This demonstrates the success of the implementation of lockdown in reducing the value of the basic reproduction number. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

Transmissibility of asymptomatic COVID-19: Data from Japanese clusters.

BACKGROUND: The epidemiological importance of asymptomatic individuals who would never develop illness, compared to those who eventually develop symptoms, has yet to be fully clarified. METHODS: The very first cluster data in Tokyo and Kanagawa (n = 36) were analyzed. Movement of all close contact was restricted for 14 days and they underwent laboratory testing with polymerase chain reaction. The reproduction numbers of symptomatic and asymptomatic cases were estimated. RESULTS: The reproduction number for symptomatic cases was estimated to be 1.2 (95% confidence interval (CI): 0.5-2.9). The relative infectiousness of asymptomatically infected cases was estimated to be 0.27 (95% CI: 0.03-0.81) of symptomatic cases. CONCLUSION: The relative transmissibility of asymptomatic cases is limited. Observing clusters starting with symptomatic transmission might be sufficient for the control.

The basic reproduction number of the new coronavirus pandemic with mortality for India, the Syrian Arab Republic, the United States, Yemen, China, France, Nigeria and Russia with different rate of cases.

BACKGROUND: The basic reproduction number values give an initial prediction of the disease because the values predict of end of the disease if the values are less than one or the disease converts to epidemic if the values are more than one. We apply the SIRD epidemiology model for estimating the basic reproduction number of the new coronavirus disease for multiple different countries. METHODS: For estimating of the basic reproduction number values, we fit the SIRD model using the Runge-Kutta simulation method in addition to the analytical solution of parts of the model. We use the collected data of the new coronavirus pandemic reported up to date July 30, 2020 in India, the Syrian Arab Republic, the United States, France, Nigeria, Yemen, China and Russia. RESULTS: We find that the basic reproduction numbers of the new coronavirus disease are located in the range [1.0011-2.7936] for the different location countries and the values of the ratio between the rate of recovery and the rate of mortality are between 1.5905 for Yemen and 44.0805 for Russia. Also, we find the dates of the actual decreasing of Covid-19 cases in five countries. CONCLUSIONS: We find that the basic reproductive number is between 1.0011 for the smallest value and 2.7936 for the greatest value. The most important thing is that the values of the basic reproduction number of the new coronavirus disease in all considered countries are more than one which means that the new coronavirus disease is epidemic in all of considered countries.