Mathematical Predictions for Covid-19 as a Global Pandemic (Preprint)

2020 ◽  
Author(s):  
Alexander Okhuese Victor
Keyword(s):  
Recovery Rate ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Policy Makers ◽  
Infected Population ◽  
Global Pandemic ◽  
Secondary Infections ◽  
Rate Of Recovery ◽  
Precautionary Measures ◽  
Model Equations

UNSTRUCTURED The model equations which exhibits the disease-free equilibrium (E_0 ) state for COVID-19 coronavirus does not exist and hence does not satisfy the criteria for a locally or globally asymptotic stability when the basic reproductive number R_0=1 for and endemic situation. This implies that the COVID-19 coronavirus does not have a curative vaccine yet and precautionary measures are advised through quarantine and observatory procedures. The basic reproductive number was found to be R_0<1 and hence shows that there is a chance of decline of secondary infections when the ratio between the incidence rate in the population and the total number of infected population quarantined with observatory procedure. Furthermore, numerical simulations were carried to complement the analytical results in investigating the effect of the implementation of quarantine and observatory procedures has on the projection of the further spread of the virus globally. Result shows that the proportion of infected population in the absence of curative vaccination will continue to grow globally meanwhile the recovery rate will continue slowly which therefore means that the ratio of infection to recovery rate will determine the death rate that is recorded globally. Therefore, the effort to evaluate the disease equilibrium shows that unless there is a dedicated effort from individual population, government, health organizations, policy makers and stakeholders, the world would hardly be reed of the COVID-19 coronavirus and further spread is eminent and the rate of infection will continue to increase despite the increased rate of recovery until a curative vaccine is developed.

scholarly journals MATHEMATICAL PREDICTIONS FOR COVID-19 AS A GLOBAL PANDEMIC

2020 ◽  
Author(s):  
Victor Alexander Okhuese
Keyword(s):  
Decision Makers ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Government Decision ◽  
Global Pandemic ◽  
Secondary Infections ◽  
Rate Of Recovery ◽  
Precautionary Measures ◽  
The Moment ◽  
Disease Free

ABSTRACTThis study shows that the disease free equilibrium (E0) for COVID-19 coronavirus does not satisfy the criteria for a locally or globally asymptotic stability. This implies that as a pandemic as declared by WHO (2020) the COVID-19 coronavirus does not have a curative vaccine yet and precautionary measures are advised through quarantine and observatory procedures. Also, the Basic Reproductive number (R0 < 1) by Equation (33) shows that there is a chance of decline of secondary infections when the ratio between the incidence rate in the population and the total number of infected population quarantined with observatory procedure.The effort to evaluate the disease equilibrium shows that unless there is a dedicated effort from government, decision makers and stakeholders, the world would hardly be reed of the COVID-19 coronavirus and further spread is eminent and the rate of infection will continue to increase despite the increased rate of recovery because of the absence of vaccine at the moment.

scholarly journals Estimation of the probability of reinfection with COVID-19 coronavirus by the SEIRUS model

2020 ◽  
Author(s):  
Victor Alexander Okhuese
Keyword(s):  
Recovery Rate ◽  
Death Rate ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Chain Reaction ◽  
Health Community ◽  
Polymerase Chain ◽  
Model Equations ◽  
Disease Free ◽  
Pcr Test

AbstractWith sensitivity of the Polymerase Chain Reaction (PCR) test used to detect the presence of the virus in the human host, the global health community has been able to record a great number of recovered population. Therefore, in a bid to answer a burning question of reinfection in the recovered class, the model equations which exhibits the disease-free equilibrium (E0) state for COVID-19 coronavirus was developed in this study and was discovered to both exist as well as satisfy the criteria for a locally or globally asymptotic stability with a basic reproductive number R0 = 0 for and endemic situation. Hence, there is a chance of no secondary reinfections from the recovered population as the rate of incidence of the recovered population vanishes, that is, B = 0.Furthermore, numerical simulations were carried to complement the analytical results in investigating the effect of the implementation of quarantine and observatory procedures has on the projection of the further spread of the virus globally. Result shows that the proportion of infected population in the absence of curative vaccination will continue to grow globally meanwhile the recovery rate will continue slowly which therefore means that the ratio of infection to recovery rate will determine the death rate that is recorded globally and most significant for this study is the rate of reinfection by the recovered population which will decline to zero over time as the virus is cleared clinically from the system of the recovered class.

scholarly journals Estimation of the Probability of Reinfection With COVID-19 by the Susceptible-Exposed-Infectious-Removed-Undetectable-Susceptible Model (Preprint)

2020 ◽  
Author(s):  
Alexander Victor Okhuese
Keyword(s):  
Recovery Rate ◽  
Basic Reproductive Number ◽  
Polymerase Chain Reaction Test ◽  
Reproductive Number ◽  
Health Community ◽  
Existence And Stability ◽  
Polymerase Chain ◽  
Model Equations ◽  
Chain Reaction Test ◽  
Disease Free

BACKGROUND With the sensitivity of the polymerase chain reaction test used to detect the presence of the virus in the human host, the worldwide health community has been able to record a large number of the recovered population. OBJECTIVE The aim of this study was to evaluate the probability of reinfection in the recovered class and the model equations, which exhibits the disease-free equilibrium state for the coronavirus disease. METHODS The model differential equation was evaluated for the disease-free equilibrium for the case of reinfection as well as the existence and stability criteria for the disease, using the model proportions. This evaluation shows that the criteria for a local or worldwide asymptotic stability with a basic reproductive number (<i>R</i><sub>0</sub>=0) were satisfied. Hence, there is a chance of no secondary reinfections from the recovered population, as the rate of incidence of the recovered population vanishes (ie, <i>B</i>=0). RESULTS With a total of about 900,000 infected cases worldwide, numerical simulations for this study were carried out to complement the analytical results and investigate the effect that the implementation of quarantine and observation procedures has on the projection of further virus spread. CONCLUSIONS As shown by the results, the proportion of the infected population, in the absence of a curative vaccination, will continue to grow worldwide; meanwhile, the recovery rate will continue slowly, which means that the ratio of infection rate to recovery rate will determine the death rate that is recorded. Most significant for this study is the rate of reinfection by the recovered population, which will decline to zero over time as the virus is cleared clinically from the system of the recovered class.

scholarly journals Estimation of the Probability of Reinfection With COVID-19 by the Susceptible-Exposed-Infectious-Removed-Undetectable-Susceptible Model

10.2196/19097 ◽  
2020 ◽  
Vol 6 (2) ◽  
pp. e19097 ◽  
Author(s):  
Alexander Victor Okhuese
Keyword(s):  
Recovery Rate ◽  
Basic Reproductive Number ◽  
Polymerase Chain Reaction Test ◽  
Reproductive Number ◽  
Health Community ◽  
Existence And Stability ◽  
Polymerase Chain ◽  
Model Equations ◽  
Chain Reaction Test ◽  
Disease Free

Background With the sensitivity of the polymerase chain reaction test used to detect the presence of the virus in the human host, the worldwide health community has been able to record a large number of the recovered population. Objective The aim of this study was to evaluate the probability of reinfection in the recovered class and the model equations, which exhibits the disease-free equilibrium state for the coronavirus disease. Methods The model differential equation was evaluated for the disease-free equilibrium for the case of reinfection as well as the existence and stability criteria for the disease, using the model proportions. This evaluation shows that the criteria for a local or worldwide asymptotic stability with a basic reproductive number (R0=0) were satisfied. Hence, there is a chance of no secondary reinfections from the recovered population, as the rate of incidence of the recovered population vanishes (ie, B=0). Results With a total of about 900,000 infected cases worldwide, numerical simulations for this study were carried out to complement the analytical results and investigate the effect that the implementation of quarantine and observation procedures has on the projection of further virus spread. Conclusions As shown by the results, the proportion of the infected population, in the absence of a curative vaccination, will continue to grow worldwide; meanwhile, the recovery rate will continue slowly, which means that the ratio of infection rate to recovery rate will determine the death rate that is recorded. Most significant for this study is the rate of reinfection by the recovered population, which will decline to zero over time as the virus is cleared clinically from the system of the recovered class.

scholarly journals Transmission dynamics of SARS-COV-2 in China: impact of public health interventions

2020 ◽  
Author(s):  
Wenbao Wang ◽  
Yiqin Chen ◽  
Qi Wang ◽  
Ping Cai ◽  
Ye He ◽  
...  
Keyword(s):  
Public Health ◽  
Health Interventions ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Public Health Interventions ◽  
The Public ◽  
Global Pandemic ◽  
Actual Growth ◽  
Global Threat ◽  
The Impact

AbstractCOVID-19 has become a global pandemic. However, the impact of the public health interventions in China needs to be evaluated. We established a SEIRD model to simulate the transmission trend of China. In addition, the reduction of the reproductive number was estimated under the current forty public health interventions policies. Furthermore, the infection curve, daily transmission replication curve, and the trend of cumulative confirmed cases were used to evaluate the effects of the public health interventions. Our results showed that the SEIRD curve model we established had a good fit and the basic reproductive number is 3.38 (95% CI, 3.25–3.48). The SEIRD curve show a small difference between the simulated number of cases and the actual number; the correlation index (H2) is 0.934, and the reproductive number (R) has been reduced from 3.38 to 0.5 under the current forty public health interventions policies of China. The actual growth curve of new cases, the virus infection curve, and the daily transmission replication curve were significantly going down under the current public health interventions. Our results suggest that the current public health interventions of China are effective and should be maintained until COVID-19 is no longer considered a global threat.

scholarly journals Transmission dynamics of SARS-CoV-2 in a mid-size city of China

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Hongjun Zhao ◽  
Xiaoxiao Lu ◽  
Wenhui Lun ◽  
Tiegang Li ◽  
Boqi Rao ◽  
...  
Keyword(s):  
Case Series ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Wuhan City ◽  
The Public ◽  
Global Pandemic ◽  
Asymptomatic Patients ◽  
History Of ◽  
Multifaceted Interventions ◽  
Epidemiological Characteristics

Abstract Background An outbreak of pneumonia, COVID-19 associated with the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) emerged in Wuhan city and then rapidly spread to other cities. Wenzhou is located approximately 900 km from Wuhan, which was experiencing an outbreak that was severe at the time but is considered modest as the epidemic became a pandemic. We described the epidemiological characteristics of SARS-CoV-2 outside of the epicenter to help understand the transmission pattern in a mid-sized Chinese city. Methods To investigate the epidemiological and clinical characteristics of the COVID-19, we described case series of 473 patients with confirmed COVID-19 in Wenzhou, China from January 27 to March 16, 2020. We described the public health interventions of COVID-19 and evaluated the effect of interventions by the effective reproduction number (Rt). Results The median age of all patients was 47.6 years, 48.4% of whom were female. 33.8% of the patients had a history of residence in Wuhan. Fever (71.7%) and cough (43.1%) were the most common symptoms. In addition, three kinds of unconventional cases were observed, namely 4.9% asymptomatic patients, 7.6% confirmed patients who had no link to Wuhan city but contact with individuals from Wuhan without any symptoms at the time of contact, and 12.9% confirmed patients who had an unknown source of transmission. We estimated that the basic reproductive number (R0) was 2.75 (95% CI: 2.37–3.23). The Rt fluctuated within the range of 2.50 to 3.74 from January 11 to January 16 while gradually reached a peak of 3.74 on January 16. Rt gradually decreased after January 16 and decreased to 1.00 on January 30. Rt continually decreased and reached the lowest point (0.03) on February 21, 2020. Conclusion Our study presented the possibility of asymptomatic carriers affected with SARS-CoV-2, and transmission by these three kinds of unconventional patients in Wenzhou may be an important characteristic of SARS-CoV-2 transmission. The evaluation showed that a series of multifaceted interventions proved effective in controlling the epidemic of COVID-19. These findings might provide valuable examples of control policies for countries or areas in combatting the global pandemic of COVID-19.

scholarly journals Assessment of past Rift Valley fever outbreak using Modeling, Risk analysis and decision tree in Sudan

2020 ◽  
Author(s):  
mohamed E Ahmed ◽  
Maximilian PO Baumann ◽  
Thomas Selhorst ◽  
Tamador M Abdellah ◽  
Atif A Abdelgadir
Keyword(s):  
Risk Analysis ◽  
Decision Tree ◽  
Recovery Rate ◽  
Rift Valley ◽  
Rift Valley Fever ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Analysis Tool ◽  
Valley Fever ◽  
Sheep Population

Abstract Background A retrospective study was performed in selected states of the Sudan that include Gezira state, White Nile, Blue Nile, Khartoum, River Nile and Sennar states in order to determine the seroprevalence of Rift Valley Fever (RVF) and associated risk factors as well as an attempt was made to apply mapping, risk analysis tool to investigate the disease .Those epidemiological tools were used for purpose of good management strategies and policy makers as well. The source of data was epidemiological reports and archives from the Federal Ministry of Animal resources, universities and Non Governmental Organizations for outbreaks of RVF also and laboratory reports of serum samples tested by ELISA. The test performance characteristics were 99% test sensitivity and 99% test specificity.A total of 3393from, sheep, goats and cattle were sampled and selected to be examined. Estimated Seroprevalence of RVF was 0.15% (n=905) in sheep, 0.20 %( n=776) in goats and 0.13 %( n=638) in cattle respectively. Also information gathered was used to determine the distribution of the disease, transmission and recovery rate of infection over point in time. Method This study was retrospective survey designed to investigate previous outbreaks of RVF. The method used was risk analysis, modeling and decision tree to explain the distribution of chronology of the disease. Result The current study was carried out quantitative risk analysis to investigate RVF. Risk analysis revealed that RVF is likely to occur in the Sudan, and vaccination was estimated with highest rollback to reduce the seroprevalence of RVF to be unlikely with expected value of $ US 4368789. A frequency of 0.12%, 0.12% and 0.1% from cattle, goats and sheep population were entered in SIR model respectively. The adjustable parameters were susceptible, infected, recovery rate and death rate; the result concluded that the curve of susceptible(S) was declining, infected (I) was increasing; while recovered(R) was increasing. A total of 2487 mosquitoes were pooled, represented by 600 mosquitoes in the final model, recovery rate of mosquito overtime was 0.22 which is statistically not significant, (P-value =0.9825), and rate of infection was 0.83 %. In the current study, the Basic reproductive number (R0) was estimated by one. Uncertainty for RVF model was ranged between 0.01 to 610.65 with confidence of 95%. This study concluded that RVF is endemic in the Sudan.Conclusion Rift Valley Fever (RVF) is arthropod-borne viral zoonosis disease. It affects small ruminants, sheep and goats, and large ruminants like cattle and camel, and also can affect human. Rift Valley Fever virus (RVFV) belongs to the family Bunyviridae, genus Phlebovirus. The first isolation of RVFV was done in Kenya (4). RVFV is a negative sense RNA virus. RVFV genome is structured from three partites, small, medium and large. It is peracute or acute febrile disease that is characterized by numerous abortions in female and high mortality among young animals and humans. Mosquitoe is the principle vector of the disease. It is transmitted by direct contact with infected tissues or organs of animals and ingestion of uncooked or row milk (1). The study was carried out to investigate the risk related to RVF seroepidemiology and distribution of the disease among livestock and to determine the most efficient policies in management of RVF outbreak by using retrospective data, however more further serosurveillances were required to thoroughly understand the epidemiology of the disease.

scholarly journals Transmission dynamics and control strategies of COVID-19: a modelling study

2021 ◽  
Vol 102 (2) ◽  
pp. 92-105
Author(s):  
U.T. Mustapha ◽  
◽  
E. Hincal ◽  
A. Yusuf ◽  
S. Qureshi ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Recovery Rate ◽  
Transmission Rate ◽  
Face Mask ◽  
Basic Reproductive Number ◽  
Effective Control ◽  
Reproductive Number ◽  
Model Parameters ◽  
Susceptible Population ◽  
Social Distancing

In this paper a mathematical model is proposed, which incorporates quarantine and hospitalization to assess the community impact of social distancing and face mask among the susceptible population. The model parameters are estimated and fitted to the model with the use of laboratory confirmed COVID-19 cases in Turkey from March 11 to October 10, 2020. The partial rank correlation coefficient is employed to perform sensitivity analysis of the model, with basic reproduction number and infection attack rate as response functions. Results from the sensitivity analysis reveal that the most essential parameters for effective control of COVID-19 infection are recovery rate from quarantine individuals (δ1), recovery rate from hospitalized individuals (δ4), and transmission rate (β). Some simulation results are obtained with the aid of mesh plots with respect to the basic reproductive number as a function of two different biological parameters randomly chosen from the model. Finally, numerical simulations on the dynamics of the model highlighted that infections from the compartments of each state variables decreases with time which causes an increase in susceptible individuals. This implies that avoiding contact with infected individuals by means of adequate awareness of social distancing and wearing face mask are vital to prevent or reduce the spread of COVID-19 infection.

scholarly journals An SEIRS Epidemic Model with Immigration and Vertical Transmission

2020 ◽  
pp. 48-53
Author(s):  
Ruksana Shaikh ◽  
Pradeep Porwal ◽  
V. K. Gupta
Keyword(s):  
Vertical Transmission ◽  
Epidemic Model ◽  
Equilibrium Points ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Asymptotically Stable ◽  
Seirs Epidemic Model ◽  
Model Equations ◽  
The Stability ◽  
Disease Free

The study indicates that we should improve the model by introducing the immigration rate in the model to control the spread of disease. An SEIRS epidemic model with Immigration and Vertical Transmission and analyzed the steady state and stability of the equilibrium points. The model equations were solved analytically. The stability of the both equilibrium are proved by Routh-Hurwitz criteria. We see that if the basic reproductive number R0<1 then the disease free equilibrium is locally asymptotically stable and if R0<1 the endemic equilibrium will be locally asymptotically stable.

scholarly journals Epidemic Dynamics of COVID-19 Based on SEAIUHR Model Considering Asymptomatic Cases in Henan Province, China

2020 ◽  
Author(s):  
Chunyu Li ◽  
Yuchen Zhu ◽  
Chang Qi ◽  
Lili Liu ◽  
Dandan Zhang ◽  
...  
Keyword(s):  
Early Stage ◽  
Henan Province ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Infected People ◽  
Epidemic Dynamics ◽  
Global Pandemic ◽  
Prevention And Control Measures ◽  
Novel Coronavirus

Abstract Background New coronavirus disease (COVID-19), an infectious disease caused by a type of novel coronavirus, has emerged in various countries since the end of 2019 and caused a global pandemic. Many infected people went undetected because their symptoms were mild or asymptomatic, but the proportion and infectivity of asymptomatic infections remained unknown. Therefore, in this paper, we analyzed the proportion and infectivity of asymptomatic cases, as we as the prevalence of COVID-19 in Henan province. Methods We constructed SEAIUHR model based on COVID-19 cases reported from 21 January to 26 February 2020 in Henan province to estimate the proportion and infectivity of asymptomatic cases, as we as the change of effective reproductive number, \({R}_{t}\). At the same time, we simulated the changes of cases in different scenarios by changing the time and intensity of the implementation of prevention and control measures. Results The proportion of asymptomatic cases among COVID-19 infected individuals was 42% and infectivity of asymptomatic cases was 10% of that symptomatic ones. The basic reproductive number\({R}_{0}\)=2.73, and \({R}_{t}\) dropped below 1 on 1 February under a series of measures. If measures were taken five days earlier, the number of cases would be reduced by 2/3, and after 5 days the number would more than triple. Conclusions In Henan Province, the COVID-19 epidemic spread rapidly in the early stage, and there were a large number of asymptomatic infected individuals with relatively low infectivity. However, the epidemic was quickly brought under control with national measures, and the earlier measures were implemented, the better.

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