Mathematics for Infectious Diseases; Deterministic Models: A Key

2015 ◽  
Vol 7 (1) ◽  
Author(s):  
Manindra Kumar Srivastava ◽  
Purnima Srivastava
Keyword(s):  
Infectious Diseases ◽  
Mathematical Models ◽  
Whooping Cough ◽  
Deterministic Models ◽  
Ancient India ◽  
Current Information ◽  
Clear Description ◽  
Methods Of Control

The occurrence of infectious diseases was the principle reason for the demise of the ancient India. The main infectious diseases were smallpox, measles, influenza and typhus. There were also other diseases such as whooping cough, the mumps and diphtheria. It would be very difficult to obtain current information regarding important diseases, methods of transmission, methods of control and the likes. Since the wrong theories or knowledge have hindered advances in understanding. Therefore, this paper seeks to give a simple and clear description of mathematical models for infectious diseases. It has become important tools in understanding the fundamental mechanisms that drive the spread of infectious diseases.

scholarly journals Estimating the distribution of time to extinction of infectious diseases in mean-field approaches

2020 ◽  
Author(s):  
Maryam Aliee ◽  
Kat S. Rock ◽  
Matt J. Keeling
Keyword(s):  
Infectious Diseases ◽  
Stochastic Models ◽  
Mean Field ◽  
Practical Method ◽  
Deterministic Models ◽  
Recovery Processes ◽  
Time To Extinction ◽  
And Control ◽  
Field Approaches ◽  
Birth Death

AbstractA key challenge for many infectious diseases is to predict the time to extinction under specific interventions. In general this question requires the use of stochastic models which recognise the inherent individual-based, chance-driven nature of the dynamics; yet stochastic models are inherently computationally expensive, especially when parameter uncertainty also needs to be incorporated. Deterministic models are often used for prediction as they are more tractable, however their inability to precisely reach zero infections makes forecasting extinction times problematic. Here, we study the extinction problem in deterministic models with the help of an effective “birth-death” description of infection and recovery processes. We present a practical method to estimate the distribution, and therefore robust means and prediction intervals, of extinction times by calculating their different moments within the birth-death framework. We show these predictions agree very well with the results of stochastic models by analysing the simplified SIS dynamics as well as studying an example of more complex and realistic dynamics accounting for the infection and control of African sleeping sickness (Trypanosoma brucei gambiense).

scholarly journals Human factors in emerging infectious diseases

2021 ◽  
Vol 2 (1) ◽  
pp. 21-29 ◽  
Author(s):  
Scott B. Halstead
Keyword(s):  
Infectious Disease ◽  
Infectious Diseases ◽  
Human Factors ◽  
Emerging Infectious Diseases ◽  
Emerging Infectious Disease ◽  
Emerging Disease ◽  
Human Behaviour ◽  
Microbial World ◽  
Underlying Causes ◽  
Methods Of Control

When the underlying causes and mechanisms of emerging infectious disease problems are studied carefully, human behaviour is often involved. Even more often, the only methods of control or prevention available are to change human behaviour. Several major recent emerging disease problems can be cited. It is sometimes emphasized that it is human carelessness, human excesses, human ignorance or human habits of conquest or leisure which contribute directly to the biological niches that microorganisms are all too capable of exploiting. We must look at ourselves as the engines of microbial opportunism. It is not likely that we will ever conquer the microbial world;we must look instead to control the human factors that contribute to emergence.

scholarly journals ON THE ISSUE OF PLANNING SOWING AGRICULTURAL CROPS WITH THE MINIMUM RISK UNDER THE PRESENCE OF VARIOUS AGROCLIMATIC CONDITIONS

2021 ◽  
Vol 1 ◽  
pp. 72-83
Author(s):  
Sharif E. Guseynov ◽  
Sergey Matyukhin ◽  
Misir J. Mardanov ◽  
Jekaterina V. Aleksejeva ◽  
Olga Sidorenko
Keyword(s):  
Mathematical Models ◽  
Analytical Solutions ◽  
Probabilistic Model ◽  
Probabilistic Approach ◽  
Minimal Risk ◽  
Agricultural Crops ◽  
Deterministic Approach ◽  
Deterministic Models ◽  
Minimum Risk ◽  
Sown Area

The present paper deals with one problem of quantitative controlling the seeding of the sown area by agricultural crops in different agroclimatic conditions. The considered problem is studied from the standpoint of three strategies: from the seeding planning perspective aiming at minimal risk associated with possible unfavourable agroclimatic conditions (a probabilistic approach is used); from the perspective of obtaining the maximum crops sales profit (a deterministic approach is used); from the perspective of obtaining the maximum crops harvest. For the considered problem, mathematical models are constructed (one probabilistic model and two deterministic models, respectively), their analytical solutions are found, and then, using a specific example, the application of the constructed and solved mathematical models is illustrated as well as the obtained numerical results are analysed..

scholarly journals Influencing public health policy with data-informed mathematical models of infectious diseases: Recent developments and new challenges

Epidemics ◽  
2020 ◽  
Vol 32 ◽  
pp. 100393 ◽  
Author(s):  
Amani Alahmadi ◽  
Sarah Belet ◽  
Andrew Black ◽  
Deborah Cromer ◽  
Jennifer A. Flegg ◽  
...  
Keyword(s):  
Public Health ◽  
Health Policy ◽  
Infectious Diseases ◽  
Mathematical Models ◽  
Public Health Policy ◽  
Recent Developments ◽  
New Challenges ◽  
Data Informed

Practical models for the care of HIV and AIDS patients

1996 ◽  
Vol 7 (2) ◽  
pp. 91-97 ◽  
Author(s):  
S. C. Brailsford ◽  
R. Basu Roy ◽  
A. K. Shahani ◽  
S. Sivapalan
Keyword(s):  
Decision Making ◽  
Infectious Diseases ◽  
Mathematical Models ◽  
Resource Use ◽  
Health Professionals ◽  
Operational Research ◽  
Resource Planning ◽  
Hiv And Aids ◽  
Operational Modelling ◽  
Aid Decision

Mathematical models for infectious diseases are of lim ited use in providing practical help to health professionals. In this paper we discuss computer models developed jointly by operational research mathematicians and clinicians to meet this need. W e use the term 'operational modelling' to describe this pragm atic approach. The models can aid decision-making at a resource planning level and can also be used by clinicians to monitor and im prove patient care. The models incorporate uncertainty and variability and are therefore mathematically complex, but are easy to use and provide a great deal of useful information about morbidity and resource use.

scholarly journals Gallstone disease in children and comorbiditi

2021 ◽  
Vol 66 (3) ◽  
pp. 34-39
Author(s):  
S. Yu. Matalayeva
Keyword(s):  
Metabolic Syndrome ◽  
Infectious Diseases ◽  
Metabolic Disorders ◽  
Gallstone Disease ◽  
Comorbid Conditions ◽  
Causal Factors ◽  
Current Information ◽  
Mechanisms Of Formation ◽  
Adults And Children

The article provides current information on comorbid diseases in both adults and children with cholelithiasis. It describes their pathogenetic relationship with the formation of gallstones. The authors highlight the causal factors in the development of both gallstone disease and accompanying comorbid conditions. They demonstrate the generality of metabolic disorders in cholelithiasis and metabolic syndrome. The article describes the mechanisms of formation of both cholesterol and pigmented gallstones, which can be formed against the background of both somatic and infectious diseases. The article shows the role of drugs in the formation of gallstones. The authors substantiate the necessity of an individual approach and the development of personalized methods of prevention and treatment of cholelithiasis in children.

scholarly journals Disease Detectives: Using Mathematics to Forecast the Spread of Infectious Diseases

2021 ◽  
Vol 8 ◽  
Author(s):  
Heather Z. Brooks ◽  
Unchitta Kanjanasaratool ◽  
Yacoub H. Kureh ◽  
Mason A. Porter
Keyword(s):  
Mathematical Model ◽  
Infectious Diseases ◽  
Mathematical Models ◽  
Human Behavior ◽  
Government Policies ◽  
Disease Spread

The COVID-19 pandemic has led to significant changes in how people are currently living their lives. To determine how to best reduce the effects of the pandemic and start reopening communities, governments have used mathematical models of the spread of infectious diseases. In this article, we introduce a popular type of mathematical model of disease spread. We discuss how the results of analyzing mathematical models can influence government policies and human behavior, such as encouraging mask wearing and physical distancing to help slow the spread of a disease.

scholarly journals Optimization of Precontrol Methods and Analysis of a Dynamic Model for Brucellosis: Model Development and Validation (Preprint)

2020 ◽  
Author(s):  
Yihao Huang ◽  
Mingtao Li
Keyword(s):  
Infectious Diseases ◽  
Mathematical Models ◽  
Rapid Development ◽  
Transmission Model ◽  
Dynamic Threshold ◽  
Key Populations ◽  
Human Beings ◽  
Chinese People ◽  
Theoretical Support ◽  
Number Of Patients

BACKGROUND Brucella is a gram-negative, nonmotile bacterium without a capsule. The infection scope of Brucella is wide. The major source of infection is mammals such as cattle, sheep, goats, pigs, and dogs. Currently, human beings do not transmit Brucella to each other. When humans eat Brucella-contaminated food or contact animals or animal secretions and excretions infected with Brucella, they may develop brucellosis. Although brucellosis does not originate in humans, its diagnosis and cure are very difficult; thus, it has a huge impact on humans. Even with the rapid development of medical science, brucellosis is still a major problem for Chinese people. Currently, the number of patients with brucellosis in China is 100,000 per year. In addition, due to the ongoing improvement in the living standards of Chinese people, the demand for meat products has gradually increased, and increased meat transactions have greatly promoted the spread of brucellosis. Therefore, many researchers are concerned with investigating the transmission of Brucella as well as the diagnosis and treatment of brucellosis. Mathematical models have become an important tool for the study of infectious diseases. Mathematical models can reflect the spread of infectious diseases and be used to study the effect of different inhibition methods on infectious diseases. The effect of control measures to obtain effective suppression can provide theoretical support for the suppression of infectious diseases. Therefore, it is the objective of this study to build a suitable mathematical model for brucellosis infection. OBJECTIVE We aimed to study the optimized precontrol methods of brucellosis using a dynamic threshold–based microcomputer model and to provide critical theoretical support for the prevention and control of brucellosis. METHODS By studying the transmission characteristics of Brucella and building a Brucella transmission model, the precontrol methods were designed and presented to the key populations (Brucella-susceptible populations). We investigated the utilization of protective tools by the key populations before and after precontrol methods. RESULTS An improvement in the amount of glove-wearing was evident and significant (<i>P</i>&lt;.001), increasing from 51.01% before the precontrol methods to 66.22% after the precontrol methods, an increase of 15.21%. However, the amount of hat-wearing did not improve significantly (<i>P</i>=.95). Hat-wearing among the key populations increased from 57.3% before the precontrol methods to 58.6% after the precontrol methods, an increase of 1.3%. CONCLUSIONS By demonstrating the optimized precontrol methods for a brucellosis model built on a dynamic threshold–based microcomputer model, this study provides theoretical support for the suppression of Brucella and the improved usage of protective measures by key populations.

Sign in / Sign up

Export Citation Format

Share Document