scholarly journals Contributions to the mathematical theory of epidemics: V. Analysis of experimental epidemics of mouse-typhoid; a bacterial disease conferring incomplete immunity

1939 ◽  
Vol 39 (3) ◽  
pp. 271-288 ◽  
Author(s):  
W. O. Kermack ◽  
A. G. McKendrick
Keyword(s):  
General Theory ◽  
Observational Data ◽  
Life Table ◽  
Infection Rate ◽  
Recovery Rate ◽  
Death Rate ◽  
Mathematical Theory ◽  
Bacterial Disease ◽  
Experimental Conditions ◽  
Published Paper

In a recently published paper (Kermack & McKendrick, 1937) the observational data relating to epidemics of ectromelia in populations of mice maintained under experimental conditions (Greenwood et al. 1936) has been analysed in the light of a mathematical theory of epidemics developed by us during recent years (Kermack & McKendrick, 1927, 1932, 1933, 1936). It was shown that the life table giving the chance of mice surviving for various lengths of time in infected communities is very closely represented by a formula calculated on the assumption that the various rates—infection rate, recovery rate, death rate, etc.—are constants. It is, of course, realized that this simplifying assumption can only be regarded as approximately true. It renders the application of the general theory practicable, and the result of the investigation justifies its use, in so far as the theory so simplified does actually conform to the experimental results.

scholarly journals Determining COVID-19 Dynamics Using Physics Informed Neural Networks

2021 ◽  
Author(s):  
Joseph Malinzi ◽  
Simanga Gwebu ◽  
Sandile Motsa
Keyword(s):  
Neural Networks ◽  
Mathematical Model ◽  
Infection Rate ◽  
Recovery Rate ◽  
Death Rate ◽  
System Of Equations ◽  
Governing System

The Physics Informed Neural Networks framework is applied to the understanding of the dynamics of Coronavirus of 2019. To provide the governing system of equations used by the framework, the Susceptible-Infected-Recovered-Death mathematical model is used. The study focused on finding the patterns of the dynamics of the disease which involves predicting the infection rate, recovery rate and death rate; thus predicting the active infections, total recovered, susceptible and deceased at any required time. The study used data that was collected on the dynamics of COVID-19 from the Kingdom of Eswatini between March 2020 and September 2021. The obtained results showed less errors thus making highly accurate predictions.

scholarly journals System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 787
Author(s):  
Olaniyi Iyiola ◽  
Bismark Oduro ◽  
Trevor Zabilowicz ◽  
Bose Iyiola ◽  
Daniel Kenes
Keyword(s):  
Fractional Order ◽  
Recovery Rate ◽  
Death Rate ◽  
Numerical Solutions ◽  
Complex Nature ◽  
Uniqueness Of Solutions ◽  
Fractional Equations ◽  
Effective Contact ◽  
Proposed Model ◽  
Fractional Models

The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalizations and deaths have been observed, with thousands of cases occurring daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to better understand the transmission of the disease. Non-locality in the model has made fractional differential equations appropriate for modeling. Solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate, quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, and recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium (symmetry), and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam–Bashforth–Moulton method developed for the fractional-order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19. Based on the results with different fractional-order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is currently occurring in many countries.

A N. Bourbaki Type General Theory and the Properties of Contracting Symbols and Corresponding Contracted Forms

1999 ◽  
Vol 6 (2) ◽  
pp. 179-190
Author(s):  
SH. Pkhakadze
Keyword(s):  
General Theory ◽  
Mathematical Theory ◽  
General Mathematical Theory

Abstract A system of contracting symbols is introduced for a N. Bourbaki type general mathematical theory corresponding to a general classical mathematical theory .

Public Asylum Reports for 1873

1874 ◽  
Vol 20 (91) ◽  
pp. 464-471
Keyword(s):  
Recovery Rate ◽  
Death Rate ◽  
Annual Report

Newcastle-on-Tyne.—Ninth Annual Report.—Mr. Wickham enters into the following defence of Australian tinned meats, which they, perhaps, hardly required:—“The Australian tinned meats, which are now freely used, at first met with much opposition, and, even now, a few of the more ill-humoured patients object to them. To some of the better disposed ones the flavour is at first a little disagreeable, but the same may be said of fairly intelligent people outside, and they are so very few here that it is impossible to consider them in the arrangement of a diet table. As for its nutritious qualities, I have only to say that the patients eating it (excluding those suffering from wasting diseases) gain, or at least retain, their weight. The recovery rate for the three years I have held office has been 45 9 per cent. as against 33 5 per cent. during the previous five years, and the death rate has been steadily decreasing, while the necessity for ordering extras for the sick is reduced to the very lowest minimum. The Australian meat has been largely used during that time, and, though I do not wish to ascribe these satisfactory results to its agency, it must be apparent that it has not interfered with the primary objects of the institution.”

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 Higher Mortality and Infection Rate in a Region or Country Suggest a Longer Time of COVID-19 Disease Pandemic

2020 ◽  
Author(s):  
Tianshu Gu ◽  
Lan Yao ◽  
Tong Sun ◽  
Sara W. Day ◽  
Scott C. Howard ◽  
...  
Keyword(s):  
Infection Rate ◽  
Death Rate ◽  
Positive Relationship ◽  
Disease Duration ◽  
Strong Positive Correlation ◽  
Positive Correlation ◽  
Number Of Patients ◽  
The World ◽  
Total Death ◽  
R Value

Abstract In view of the fact that the 2019-nCoV has spread to most countries in the world, it is necessary to make scientific and well-founded predictions of the current pandemic situation caused by the virus worldwide, which are conducive to public, social and government responses that mitigate and appropriately address the pandemic. We collected data from provinces with more than 200 cases in China and from eight other countries. Our analyses showed that the disease duration has no correlation with the number of patients, with r = 0.184. The number of deaths was not correlated to the disease duration, with r = 0.242. However, a positive correlation between the days of disease duration and infection rate, with a r = 0.626. Furthermore, there is a strong positive correlation between the disease duration and total death rate, with a r = 0.707. Using death rate of first 25 days, we obtained a positive relationship with a r value of 0.597. Based on the data from first 25 days, the minimum and maximum days of COVID-19 pandemic duration of eight countries was estimated between days of 37 and 114 days.

scholarly journals Data granularity in mid-year life table construction

2020 ◽  
Author(s):  
Jose M Pavia ◽  
Natalia Salazar ◽  
Josep Lledo
Keyword(s):  
Big Data ◽  
Life Table ◽  
Death Rate ◽  
Life Tables ◽  
Population Estimates ◽  
Substantial Influence ◽  
Pension Systems ◽  
Insurance Policies ◽  
Statistical Agencies ◽  
Data Granularity

Life tables have a substantial influence on both public pension systems andlife insurance policies. National statistical agencies construct life tables fromhypotheses death rate estimates to the (mx aggregated ), or death figures probabilities of demographic (q x ), after applying events (deaths, variousmigrations and births). The use of big data has become extensive acrossmany disciplines, including population statistics. We take advantage of thisfact to create new (more unrestricted) mortality estimators within the familyof period-based estimators, in particular, when the exposed-to-riskpopulation is computed through mid-year population estimates. We useactual data of the Spanish population to explore, by exploiting the detailedmicrodata of births, deaths and migrations (in total, more than 186 milliondemographic events), the effects that different assumptions have oncalculating death probabilities. We also analyse their impact on a sample ofinsurance product. Our results reveal the need to include granular data,including the exact birthdate of each person, when computing period mid-year life tables.

scholarly journals A predictive model for Covid-19 spread – with application to eight US states and how to end the pandemic

2020 ◽  
Vol 148 ◽  
Author(s):  
Z. S. Khan ◽  
F. Van Bussel ◽  
F. Hussain
Keyword(s):  
Predictive Model ◽  
Release Rate ◽  
Recovery Rate ◽  
Death Rate ◽  
Compartmental Model ◽  
Contact Rate ◽  
Reinfection Rate ◽  
Us States ◽  
Coupled Equations ◽  
The Us

Abstract A compartmental model is proposed to predict the coronavirus 2019 (Covid-19) spread. It considers: detected and undetected infected populations, social sequestration, release from sequestration, plus reinfection. This model, consisting of seven coupled equations, has eight coefficients which are evaluated by fitting data for eight US states that make up 43% of the US population. The evolution of Covid-19 is fairly similar among the states: variations in contact and undetected recovery rates remain below 5%; however, variations are larger in recovery rate, death rate, reinfection rate, sequestration adherence and release rate from sequestration. Projections based on the current situation indicate that Covid-19 will become endemic. If lockdowns had been kept in place, the number of deaths would most likely have been significantly lower in states that opened up. Additionally, we predict that decreasing contact rate by 10%, or increasing testing by approximately 15%, or doubling lockdown compliance (from the current ~15% to ~30%) will eradicate infections in Texas within a year. Extending our fits for all of the US states, we predict about 11 million total infections (including undetected), and 8 million cumulative confirmed cases by 1 November 2020.

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