Mathematical Epidemiology in Medicine & Social Sciences

Dear Colleagues,

The transmission of infectious diseases has traditionally been modelled by coupled differential equations, which usually gives rise to simple patterns of activity, including pandemic outbreaks, forced seasonal periodic incidence or constant persistent levels of infection. This classical approach has dominated the field of mathematical epidemiology since the beginning of the past century. However, many problems in epidemiology involve a large but finite number of individuals or cells, each of them with a set of attributes and characteristics that we must take into account for the efficient and realistic modelling of the disease at hand. Targeting specific populations during vaccination campaigns or social groups involved in pernicious addictions can only be adequately simulated by considering discrete models instead of the usual compartmental approach. One way to achieve this goal is by means of defining an underlying discrete structure in which single units, representing the individuals, are connected among each other according to a specific distribution of links, i. e., by resorting to the theory of complex networks. Elucidating the real structure of these complex networks in the case of human populations has become a hot topic of fundamental importance for epidemic disease prevention and control.

On the other hand, understanding epidemiological models can often better be achieved with continuous differential equations models in which we can use all the results for the mathematical theory of these systems. Fractional differential equation models can also provide another perspective for modelling other diseases in which a memory effect could be fundamental for obtaining predictions on the evolution of the epidemics. Recently, exact results for the susceptible–recovered–infected (SIR) model have also be obtained, contributing to a deeper comprehension of the nature of these models and their possibilities for practical applications.

The purpose of this Special Issue is to publish cutting-edge and original research papers addressing recent advances in the continuous and discrete modelling of mathematical epidemiology problems in infectious diseases and social contagion. We seek, in particular, papers in which the successful application of these mathematical models in a multidisciplinary environment is clearly described, but also new general results on the theory of mathematical models in epidemiology.

Dr. Luis Acedo Rodríguez
Guest Editor

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• Random networks in population studies
• Discrete models in epidemiology
• Exact results for continuous models in epidemiology
• Social models for addictive behavior
• Discrete modelling for the prevention and control of plagues
• Competition Lotka–Volterra models for infectious diseases
• Discrete fractional calculus applications to epidemiology
• Discrete and continuous approaches to seasonal patterns of infection
• Agent-based modelling