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How does mathematics reveal the mystery of the epidemic? Reveal the power of infectious disease models!
With the COVID-19 pandemic raging around the world, governments and public health agencies around the world are in urgent need of effective ways to predict the trend of the epidemic and the effectiveness of control measures. Due to its importance in infectious disease research, mathematical models have become a key tool for researchers to respond to epidemics. From early analysis of causes of death to today's complex virus transmission models, the application of mathematical models in public health has gone through hundreds of years, but has continued to evolve and develop.
Mathematical models can not only predict the development of the epidemic, but also help formulate effective public health response strategies.
The history of mathematical models
Beginning with John Graunt in the 17th century, scientists began to try to quantify the causes of death. Grant's research is considered the beginning of "competing risk theory". Subsequently, mathematical models continued to evolve over time, especially the mathematical modeling conducted by Daniel Bernoulli in 1760, which successfully provided information for vaccination and epidemic prevention. theoretical basis.
As time passed and entered the 20th century, William Hamer and Ronald Ross used the law of quality behavior to explain epidemic behavior, forming the later Kermack–McKendrick and Reed –Frost infectious disease model, laying the foundation for subsequent epidemic models.
Assumptions and limitations of the model
While mathematical models can provide valuable predictions, their accuracy often depends on the assumptions made. For example, the "homogeneous mixture" hypothesis is one of the few simplifying assumptions that can be established when treating a metropolis like Tokyo, just like how groups with different social structures interact. Therefore, model results often need to be adjusted according to real-life conditions.
Basing a model on unrealistic assumptions affects its predictive accuracy.
Types of epidemic models
Epidemiological models can be divided into stochastic models and deterministic models. Stochastic models take into account the randomness among variables, while deterministic models provide more precise mathematical expressions when dealing with large populations, such as the prediction of tuberculosis infection.
At the same time, there are also dynamic and mean field models, which fully consider the impact of social structure on the spread of the epidemic and take individual behavioral factors into consideration.
Basic infection number and persistence status
The basic infection number (R0) is a key indicator to evaluate whether an infectious disease can spread. When R0 is greater than 1, it means that each infected person can infect more than one new person; conversely, when R0 is less than 1, the epidemic will gradually fade. This indicator can not only help public health experts understand the potential impact of the epidemic, but also guide vaccination and herd immunity strategies.
R0 is an important indicator for determining whether the epidemic can be sustained.
Application and impact of practical models
Today, more and more complex models, such as agent models (ABMs), are being used to simulate the transmission dynamics of SARS-CoV-2 to assist public health decision-making. Although their construction process is complex and computationally demanding, accurate models can still provide valuable insights into future epidemic prevention strategies, especially in making epidemic predictions and evaluating the effectiveness of control policies. We often see governments around the world basing decisions on policy directions such as lockdowns, social distancing and vaccination planning based on these models.
Future Prospects of Mathematical Models
With the advancement of science and technology and the development of data analysis technology, the role of mathematical models in epidemic research will become increasingly important. Future models will not only be limited to basic analysis of infectious diseases, but can also further integrate elements of bioinformatics, social networks, and psychological behavior to more accurately simulate crowd behavior and virus transmission patterns.
Facing future epidemic challenges, what new breakthroughs and changes do you think mathematical models can bring?
