TRANSMISSION DYNAMICS AND CONTROL STRATEGIES OF COVID-19 IN WUHAN, CHINA

2020 ◽  
Vol 28 (03) ◽  
pp. 543-560 ◽  
Author(s):  
LIUYONG PANG ◽  
SANHONG LIU ◽  
XINAN ZHANG ◽  
TIANHAI TIAN ◽  
ZHONG ZHAO
Keyword(s):  
Reproduction Number ◽  
Control Strategies ◽  
Public Awareness ◽  
Control Measures ◽  
Transmission Dynamics ◽  
Published Data ◽  
Model Parameters ◽  
Strict Control ◽  
Dynamics And Control ◽  
Numerical Calculation Method

In December 2019, a novel coronavirus, SARS-COV-2, was identified among patients in Wuhan, China. Two strict control measures, i.e., putting Wuhan on lockdown and taking strict quarantine rule, were carried out to contain the spread of COVID-19. Based on the different control measures, we divided the transmission process of COVID-19 into three stages. An SEIHR model was established to describe the transmission dynamics and was applied to fit the published data on the confirmed cases of Wuhan city from December 31, 2019 to March 25, 2020 to deduce the time when the first patient with COVID-19 appeared. The basic reproduction number was estimated in the first stage to demonstrate the number of secondary infectious cases generated by an average infectious case in the absence of policy intervention. The effective reproduction numbers in second and third stages were estimated to evaluate the effects of the two strict control measures. In addition, sensitivity analysis of the reproduction number according to model parameters was executed to demonstrate the effect of the control measures for containing the spread of COVID-19. Finally, the numerical calculation method was applied to investigate the influence of the different control measures on the spread of COVID-19. The results indicated that following the strict quarantine rule was very effective, and reducing the effective contact rates and improving the diagnosis rate were crucial in reducing the effective reproduction number, and taking control measures as soon as possible can effectively contain a larger outbreak of COVID-19. But a bigger challenge for us to contain the spread of COVID-19 was the transmission from the asymptomatic carriers, which required to raising the public awareness of self-protection and keeping a good physical protection.

scholarly journals Mathematical modelling of COVID-19 transmission and control strategies in the population of Bauchi State, Nigeria

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Yusuf Abdu Misau ◽  
Nanshin Nansak ◽  
Aliyu Maigoro ◽  
Sani Malami ◽  
Dominic Mogere ◽  
...  
Keyword(s):  
Reproduction Number ◽  
Control Strategies ◽  
Research Work ◽  
Control Measures ◽  
High Rate ◽  
World Health ◽  
Contact Tracing ◽  
Model Parameters ◽  
Deterministic System ◽  
The Novel

The novel SARS-COV-2 has since been declared a pandemic by the World Health Organization (WHO). The virus has spread from Wuhan city in China in December 2019 to no fewer than 200 countries as at June 2020 and still counting. Nigeria is currently experiencing a rapid spread of the virus amidst weak health system and more than 80% of population leaving on less than 1USD per day. To help understand the behavior of the virus in resource limited settings, we modelled the outbreak of COVID-19 and effects of control strategies in Bauchi state at north-eastern Nigeria. Using the real data of Bauchi state COVID-19 project, this research work extends the epidemic SEIR model by introducing new parameters based on the transmission dynamics of the novel COVID-19 pandemic and preventive measures. The total population of Bauchi State at the time of the study, given by is compartmentalized into five (5) different compartments as follows: Susceptible (S), Exposed (E), Infectious (I), Quarantined (Q) and Recovered (R). The new model is SEIQR. N = S → E → I → Q → R Data was collected by accessing Bauchi state electronic database of COVID-19 project to derive all the model parameters, while analysis and model building was done using Maple software. At the time of this study, it was found that the reproduction number R, for COVID-19 in Bauchi state, is 2.6 × 10-5. The reproduction number R decreased due to the application of control measures. The compartmental SEIRQ model in this study, which is a deterministic system of linear differential equations, has a continuum of disease-free equilibria, which is rigorously shown to be locallyasymptotically stable as the epidemiological threshold, known as the control reproduction number R= 0.0000026 is less than unity. The implication of this study is that the COVID-19 pandemic can be effectively controlled in Bauchi, since is R<1. Contact tracing and isolation must be increased as the models shows, the rise in infected class is a sign of high vulnerability of the population. Unless control measures are stepped up, despite high rate of recovery as shown by this study, infection rate will keep increasing as currently there is a no vaccine for COVID-19.

scholarly journals Dynamics of swine influenza model with optimal control

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Takasar Hussain ◽  
Muhammad Ozair ◽  
Kazeem Oare Okosun ◽  
Muhammad Ishfaq ◽  
Aziz Ullah Awan ◽  
...  
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Control Strategies ◽  
Influenza Pandemic ◽  
Swine Influenza ◽  
Transmission Dynamics ◽  
Model Parameters ◽  
And Control ◽  
Disease Free ◽  
Good Agreement

AbstractTransmission dynamics of swine influenza pandemic is analysed through a deterministic model. Qualitative analysis of the model includes global asymptotic stability of disease-free and endemic equilibria under a certain condition based on the reproduction number. Sensitivity analysis to ponder the effect of model parameters on the reproduction number is performed and control strategies are designed. It is also verified that the obtained numerical results are in good agreement with the analytical ones.

scholarly journals Assessing the effects of time-dependent restrictions and control actions to flatten the curve of COVID-19 in Kazakhstan

PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e10806
Author(s):  
Ton Duc Do ◽  
Meei Mei Gui ◽  
Kok Yew Ng
Keyword(s):  
Ad Hoc ◽  
Reproduction Number ◽  
National Level ◽  
Control Measures ◽  
Time Dependent ◽  
Transmission Dynamics ◽  
Model Parameters ◽  
Real World Data ◽  
Control Actions ◽  
And Control

This article presents the assessment of time-dependent national-level restrictions and control actions and their effects in fighting the COVID-19 pandemic. By analysing the transmission dynamics during the first wave of COVID-19 in the country, the effectiveness of the various levels of control actions taken to flatten the curve can be better quantified and understood. This in turn can help the relevant authorities to better plan for and control the subsequent waves of the pandemic. To achieve this, a deterministic population model for the pandemic is firstly developed to take into consideration the time-dependent characteristics of the model parameters, especially on the ever-evolving value of the reproduction number, which is one of the critical measures used to describe the transmission dynamics of this pandemic. The reproduction number alongside other key parameters of the model can then be estimated by fitting the model to real-world data using numerical optimisation techniques or by inducing ad-hoc control actions as recorded in the news platforms. In this article, the model is verified using a case study based on the data from the first wave of COVID-19 in the Republic of Kazakhstan. The model is fitted to provide estimates for two settings in simulations; time-invariant and time-varying (with bounded constraints) parameters. Finally, some forecasts are made using four scenarios with time-dependent control measures so as to determine which would reflect on the actual situations better.

scholarly journals Transmission dynamics and high infectiousness of Coronavirus Disease 2019

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Shunxiang Huang ◽  
Lin Wu ◽  
Jing Li ◽  
Ming-Zhen Xin ◽  
Yingying Wang ◽  
...  
Keyword(s):  
Reproduction Number ◽  
Control Strategies ◽  
Development Trend ◽  
Asymptomatic Infection ◽  
Control Measures ◽  
Transmission Dynamics ◽  
Natural State ◽  
Global Public Health ◽  
Natural Reproduction ◽  
The Impact

<p style='text-indent:20px;'>Coronavirus disease 2019 (COVID-19) has rapidly spread around the world since the early 2020. Recently, a second wave of COVID-19 has resurged in many countries. The transmission dynamics and infectiousness of the COVID-19 pandemic remain unclear, and developing strategies to mitigate the severity of the pandemic is a top priority for global public health. According to the infection mechanism of COVID-19, a novel susceptible-asymptomatic-symptomatic-recovered (SASR) model with control variables in a patchy environment was proposed not only to consider the key characteristics of asymptomatic infection and the effects of seasonal variation but also to incorporate different control measures for multiple transmission routes. The basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ R_{0} $\end{document}</tex-math></inline-formula> was established to describe the spreading behavior in the natural state over a long time horizon, and the natural reproduction number <inline-formula><tex-math id="M2">\begin{document}$ R_{n} $\end{document}</tex-math></inline-formula>, which describes the development trend of the disease during a short time in the future, was defined according to the actual propagation characteristics. In addition, the effective reproduction number <inline-formula><tex-math id="M3">\begin{document}$ R_{e} $\end{document}</tex-math></inline-formula> considering the control strategies was proposed to evaluate the impact of non-pharmaceutical interventions. The results of numerical simulations for COVID-19 cases in Wuhan, China, based on the SASR model indicate that <inline-formula><tex-math id="M4">\begin{document}$ R_{0} $\end{document}</tex-math></inline-formula> was 3.58, <inline-formula><tex-math id="M5">\begin{document}$ R_{n} $\end{document}</tex-math></inline-formula> ranged from 2.37 to 4.91, and <inline-formula><tex-math id="M6">\begin{document}$ R_{e} $\end{document}</tex-math></inline-formula> decreased gradually from 4.83 on December 8, 2019 to 0.31 on March 8, 2020, reaching 1.40 on January 23, 2020, when the lockdown was lifted in Wuhan. We further concluded that the total number of infections, including asymptomatic infections, was approximately 301, 804 as of March 8, 2020, in Wuhan, China. In particular, this article proposes a dynamic method to distinguish the impact of natural factors and human interventions on the development of the pandemic, and provides a theoretical basis for fighting the global COVID-19 pandemic.</p>

scholarly journals Modeling the Effects of Helminth Infection on the Transmission Dynamics of Mycobacterium tuberculosis under Optimal Control Strategies

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Aristide G. Lambura ◽  
Gasper G. Mwanga ◽  
Livingstone Luboobi ◽  
Dmitry Kuznetsov
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Drug Administration ◽  
Mass Drug Administration ◽  
Helminth Infection ◽  
Reproduction Number ◽  
Control Strategies ◽  
Active Tuberculosis ◽  
Control Measures ◽  
The Impact

A deterministic mathematical model for the transmission and control of cointeraction of helminths and tuberculosis is presented, to examine the impact of helminth on tuberculosis and the effect of control strategies. The equilibrium point is established, and the effective reproduction number is computed. The disease-free equilibrium point is confirmed to be asymptotically stable whenever the effective reproduction number is less than the unit. The analysis of the effective reproduction number indicates that an increase in the helminth cases increases the tuberculosis cases, suggesting that the control of helminth infection has a positive impact on controlling the dynamics of tuberculosis. The possibility of bifurcation is investigated using the Center Manifold Theorem. Sensitivity analysis is performed to determine the effect of every parameter on the spread of the two diseases. The model is extended to incorporate control measures, and Pontryagin’s Maximum Principle is applied to derive the necessary conditions for optimal control. The optimal control problem is solved numerically by the iterative scheme by considering vaccination of infants for Mtb, treatment of individuals with active tuberculosis, mass drug administration with regular antihelminthic drugs, and sanitation control strategies. The results show that a combination of educational campaign, treatment of individuals with active tuberculosis, mass drug administration, and sanitation is the most effective strategy to control helminth-Mtb coinfection. Thus, to effectively control the helminth-Mtb coinfection, we suggest to public health stakeholders to apply intervention strategies that are aimed at controlling helminth infection and the combination of vaccination of infants and treatment of individuals with active tuberculosis.

scholarly journals Investigating the Role of Environmental Transmission in COVID-19 Dynamics: A Mathematical Model Based Study

2020 ◽  
Author(s):  
Ibrahim M. ELmojtaba ◽  
Fatma Al-Musalhi ◽  
Asma Al-Ghassani ◽  
Nasser Al-Salti
Keyword(s):  
Mathematical Model ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Model Parameters ◽  
Environmental Transmission ◽  
Estimated Parameters ◽  
Existence And Stability

Abstract A mathematical model with environmental transmission has been proposed and analyzed to investigate its role in the transmission dynamics of the ongoing COVID-19 outbreak. Two expressions for the basic reproduction number R0 have been analytically derived using the next generation matrix method. The two expressions composed of a combination of two terms related to human to human and environment to human transmissions. The value of R0 has been calculated using estimated parameters corresponding to two datasets. Sensitivity analysis of the reproduction number to the corresponding model parameters has been carried out. Existence and stability analysis of disease free and endemic equilibrium points have been presented in relation with the obtained expressions of R0. Numerical simulations to demonstrate the effect of some model parameters related to environmental transmission on the disease transmission dynamics have been carried out and the results have been demonstrated graphically.

scholarly journals COVID-19 Pandemic in India: A Mathematical Model Study

2020 ◽  
Author(s):  
Sudhanshu Kumar Biswas ◽  
Jayanta Kumar Ghosh ◽  
Susmita Sarkar ◽  
Uttam Ghosh
Keyword(s):  
Population Density ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Virus Disease ◽  
Control Measures ◽  
High Population ◽  
Model Parameters ◽  
High Population Density ◽  
Corona Virus ◽  
Very High

The present novel corona virus (2019-nCoV) infection has created a global emergency situation by spreading all over the world in a large scale within very short time period. The infection induced death rate is also very high. There is no vaccine or anti-viral medicine for such infection. So at this moment a major worldwide problem is that how we can control this pandemic. On the other hand, India is a high population density country, where the corona virus disease (COVID-19) has started to spread from $1^{st}$ week of March, 2020 in a significant number of COVID-19 positive cases. Due to this high population density human to human social contact rate is very high in India. So control of the pandemic COVID-19 in early stage is very urgent and challenging problem. Mathematical models are employed in this paper to study the COVID-19 dynamics, to identify the influential parameters and to find the proper prevention strategies to reduce the outbreak size. In this work, we have formulated a deterministic compartmental model to study the spreading of COVID-19 and estimated the model parameters by fitting the model with reported data of ongoing pandemic in India. Sensitivity analysis has been done to identify the key model parameters. The basic reproduction number has been estimated from actual data and the effective basic reproduction number has been studied on the basis of reported cases. Some effective preventive measures and their impacts on the disease dynamics have also been studied. Future trends of the disease transmission has been Predicted from our model with some control measures. Finally, the positive measures to control the disease have been summarized.

OPTIMAL CONTROL ANALYSIS OF THE EFFECT OF TREATMENT, ISOLATION AND VACCINATION ON HEPATITIS B VIRUS

2020 ◽  
Vol 28 (02) ◽  
pp. 351-376 ◽  
Author(s):  
MUHAMMAD ALTAF KHAN ◽  
SYED AZHAR ALI SHAH ◽  
SAIF ULLAH ◽  
KAZEEM OARE OKOSUN ◽  
MUHAMMAD FAROOQ
Keyword(s):  
Optimal Control ◽  
Hepatitis B ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Control Strategies ◽  
Control Measures ◽  
Hepatitis B Infection ◽  
Control Variables ◽  
Effect Of Treatment ◽  
The Basic Reproduction Number

Hepatitis B infection is a serious health issue and a major cause of deaths worldwide. This infection can be overcome by adopting proper treatment and control strategies. In this paper, we develop and use a mathematical model to explore the effect of treatment on the dynamics of hepatitis B infection. First, we formulate and use a model without control variables to calculate the basic reproduction number and to investigate basic properties of the model such as the existence and stability of equilibria. In the absence of control measures, we prove that the disease free equilibrium is locally asymptotically stable when the basic reproduction number is less than unity. Also, using persistent theorem, it is shown that the infection is uniformly persistent, whenever the basic reproduction number is greater than unity. Using optimal control theory, we incorporate into the model three time-dependent control variables and investigate the conditions required to curtail the spread of the disease. Finally, to illustrate the effectiveness of each of the control strategies on disease control and eradication, we perform numerical simulations. Based on the numerical results, we found that the first two strategies (treatment and isolation strategy) and (vaccination and isolation strategy) are not very effective as a long term control or eradication strategy for HBV. Hence, we recommend that in order to effectively control the disease, all the control measures (isolation, vaccination and treatment) must be implemented at the same time.

scholarly journals Transmission dynamics and control measures of COVID-19 outbreak in China: a modelling study

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Xu-Sheng Zhang ◽  
Emilia Vynnycky ◽  
Andre Charlett ◽  
Daniela De Angelis ◽  
Zhengji Chen ◽  
...  
Keyword(s):  
Reproduction Number ◽  
Early Stage ◽  
Case Fatality ◽  
Control Measures ◽  
Infected People ◽  
Contact Rates ◽  
Multiple Datasets ◽  
Dynamics And Control ◽  
Successful Control ◽  
And Control

AbstractCOVID-19 is reported to have been brought under control in China. To understand the COVID-19 outbreak in China and provide potential lessons for other parts of the world, in this study we apply a mathematical model with multiple datasets to estimate the transmissibility of the SARS-CoV-2 virus and the severity of the illness associated with the infection, and how both were affected by unprecedented control measures. Our analyses show that before 19th January 2020, 3.5% (95% CI 1.7–8.3%) of  infected people were detected; this percentage increased to 36.6% (95% CI 26.1–55.4%) thereafter. The basic reproduction number (R0) was 2.33 (95% CI 1.96–3.69) before 8th February 2020; then the effective reproduction number dropped to 0.04(95% CI 0.01–0.10). This estimation also indicates that control measures taken since 23rd January 2020 affected the transmissibility about 2 weeks after they were introduced. The confirmed case fatality rate is estimated at 9.6% (95% CI 8.1–11.4%) before 15 February 2020, and then it reduced to 0.7% (95% CI 0.4–1.0%). This shows that SARS-CoV-2 virus is highly transmissible but may be less severe than SARS-CoV-1 and MERS-CoV. We found that at the early stage, the majority of R0 comes from undetected infectious people. This implies that successful control in China was achieved through reducing the contact rates among people in the general population and increasing the rate of detection and quarantine of the infectious cases.

Sign in / Sign up

Export Citation Format

Share Document