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 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 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 Mathematical modelling for malaria under resistance and population movement

2020 ◽  
Vol 38 (2) ◽  
pp. 133-163
Author(s):  
Cristhian Montoya ◽  
Jhoana P. Romero Leiton
Keyword(s):  
Human Population ◽  
Control Strategies ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Transmission Dynamic ◽  
Equilibrium Solutions ◽  
Population Movements ◽  
Existence And Stability ◽  
Theoretical Results ◽  
Disease Free

In this work, two mathematical models for malaria under resistance are presented. More precisely, the first model shows the interaction between humans and mosquitoes inside a patch under infection of malaria when the human population is resistant to antimalarial drug and mosquitoes population is resistant to insecticides. For the second model, human–mosquitoes population movements in two patches is analyzed under the same malaria transmission dynamic established in a patch. For a single patch, existence and stability conditions for the equilibrium solutions in terms of the local basic reproductive number are developed. These results reveal the existence of a forward bifurcation and the global stability of disease–free equilibrium. In the case of two patches, a theoretical and numerical framework on sensitivity analysis of parameters is presented. After that, the use of antimalarial drugs and insecticides are incorporated as control strategies and an optimal control problem is formulated. Numerical experiments are carried out in both models to show the feasibility of our theoretical results.

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.

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 A Schistosomiasis Model with Praziquantel Resistance

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Longxing Qi ◽  
Jing-an Cui
Keyword(s):  
Drug Treatment ◽  
Resistant Strain ◽  
Genetic Resistance ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Boundary Equilibrium ◽  
Existence And Stability ◽  
The Impact ◽  
Emergence Of Resistance ◽  
Disease Free

A compartmental model is established for schistosomiasis with praziquantel resistance. The model considers the impact of genetic resistance and drug treatment on the transmission of schistosomiasis. We calculate the basic reproductive number and discuss the existence and stability of disease-free equilibrium, boundary equilibrium, and coexistence equilibrium. Our analysis shows that regardless of whether drug treatment leads to the emergence of resistance, once the impact of genetic resistance is larger, the resistant strain will be dominant, which is detrimental to the control of schistosomiasis. In addition, once the proportion of human with drug-resistant strain produced by drug treatment is larger, the number of human and snails with resistant strain is larger. This is not a good result for drug treatment with praziquantel.

scholarly journals Granulocytic anaplasmosis in captive ring-tailed lemur (Lemur catta) in Poland

2021 ◽  
Vol 17 (1) ◽  
Author(s):  
Łukasz Adaszek ◽  
Anna Wilczyńska ◽  
Jerzy Ziętek ◽  
Marcin Kalinowski ◽  
Oliwier Teodorowski ◽  
...  
Keyword(s):  
Anaplasma Phagocytophilum ◽  
Polymerase Chain Reaction Test ◽  
Anaplasma Ovis ◽  
Case Presentation ◽  
Granulocytic Anaplasmosis ◽  
Pcr Product ◽  
Polymerase Chain ◽  
Obligate Intracellular Bacteria ◽  
Chain Reaction Test ◽  
Anaplasma Bovis

Abstract Background Anaplasma are obligate intracellular bacteria and aetiological agents of tick-borne diseases of both veterinary and medical interest. The genus Anaplasma comprises six species: Anaplasma marginale, Anaplasma centrale, Anaplasma ovis, Anaplasma phagocytophilum, Anaplasma bovis and Anaplasma platys. They can infect humans, carnivores, ruminants, rodents, insectivores, birds and reptiles. The aim of this study was to present the first clinical case of granulocytic anaplasmosis in a captive ring-tailed lemur in Poland. Case presentation A 4-year-old female lemur presented anorexia, epistaxis and tick infestation. The microscopic examination of a blood smear revealed morulae in neutrophils. Polymerase chain reaction test and sequencing of obtained PCR product confirmed infection by the GU183908 Anaplasma phagocytophilum strain. Therapeutic protocol included doxycycline (2.5 mg/kg p.o., b.i.d.) for 3 weeks and the lemur recovered within 24 h. Conclusions This is the first report on granulocytic anaplasmosis in a ring-tailed lemur in Europe, indicating that A. phagocytophilum infection must also be considered in differential diagnosis in this animal species, especially in individuals with thrombocytopenia associated with Ixodes ricinus parasitism.

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