Abstract
Infectious diseases are an important cause of human death. The study of the pathogenesis, spread regularity, and development trend of infectious diseases not only provides a theoretical basis for future research on infectious diseases, but also has practical guiding significance for the prevention and control of their spread. In this paper, a controlled differential equation and an objective function of infectious diseases were established by mathematical modeling. Based on cellular automata theory and a compartmental model, the SLIRDS (Susceptible-Latent-Infected-Recovered-Dead-Susceptible) model was constructed, a model which can better reflect the actual infectious process of infectious diseases. Considering the spread of disease in different populations, the model combines population density, sex ratio, and age structure to set the evolution rules of the model. Finally, on the basis of the SLIRDS model, the complex spread process of pandemic influenza A (H1N1) was simulated. The simulation results are similar to the macroscopic characteristics of pandemic influenza A (H1N1) in real life, thus the accuracy and rationality of the SLIRDS model are confirmed.
Highlights
Infectious diseases are diseases that can be transmitted from person to person, from person to animal, or from animal to animal after proto-microorganisms and parasites infect human beings or animals [1,2,3]
Based on the ability of cellular automata to model complex problems, this paper considered that, in real society, population mobility is caused by economic development, living environment, education level, and other factors, and that population density, sex ratio, and age structure of area have some influence on the spread of infectious diseases
This paper considers the effects of population density, sex ratio, and age structure on infectious disease spread in the population, and discusses the influence of different factors on infectious disease spread
Summary
Infectious diseases are diseases that can be transmitted from person to person, from person to animal, or from animal to animal after proto-microorganisms and parasites infect human beings or animals [1,2,3]. Infectivity, epidemic, and uncertainty are the three main characteristics of infectious diseases. A thorough study of the spread causes, spread routes, spread processes, and epidemic laws of infectious diseases is the main method for effective prevention, control, and elimination of infectious diseases. The mathematical study of infectious diseases is mainly based on the theory and method of infectious disease dynamics [4,5,6]. The essence of infectious disease dynamics is to establish a mathematical model that can reflect the spread process, spread law, and spread trend of infectious diseases. Its advantage is that, according to the characteristics of infectious diseases, the model of infectious diseases is reasonably assumed, the appropriate parameters are set, and the appropriate variables are selected. The dynamic characteristics of infectious diseases can be clearly revealed
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