An SIR-type epidemiological model that integrates social distancing as a dynamic law based on point prevalence and socio-behavioral factors

Abstract

Modeling human behavior within mathematical models of infectious diseases is a key component to understand and control disease spread. We present a mathematical compartmental model of Susceptible–Infectious–Removed to compare the infected curves given by four different functional forms describing the transmission rate. These depend on the distance that individuals keep on average to others in their daily lives. We assume that this distance varies according to the balance between two opposite thrives: the self-protecting reaction of individuals upon the presence of disease to increase social distancing and their necessity to return to a culturally dependent natural social distance that occurs in the absence of disease. We present simulations to compare results for different society types on point prevalence, the peak size of a first epidemic outbreak and the time of occurrence of that peak, for four different transmission rate functional forms and parameters of interest related to distancing behavior, such as: the reaction velocity of a society to change social distance during an epidemic. We observe the vulnerability to disease spread of close contact societies, and also show that certain social distancing behavior may provoke a small peak of a first epidemic outbreak, but at the expense of it occurring early after the epidemic onset, observing differences in this regard between society types. We also discuss the appearance of temporal oscillations of the four different transmission rates, their differences, and how this oscillatory behavior is impacted through social distancing; breaking the unimodality of the actives-curve produced by the classical SIR-model.

Risk Perception Influence on Vaccination Program on COVID-19 in Chile: A Mathematical Model

“…One aspect to highlight is the perception of risk ( P ) of people towards the COVID-19 pandemic. Based on [ 31 , 32 ], the associated equation is expressed by , where is defined as the rate of resistance to change, the reaction speed, and the perception of the quantified average risk. Thus, we have defined the rate of transition as dependent on the Risk Perception ( ).…”

“…One aspect to highlight is the perception of risk (P) of people towards the COVID-19 pandemic. Based on [31,32], the associated equation is expressed by P = Λ 1 (P…”

SIR model with social gatherings

“…Mathematically, the effects of social distancing and other NPIs are typically modelled by modifying the term βi in (1), known as force of infection, either by making β depend on time or some additional variable (e.g. space), or by considering a non-linear dependence on i; see for instance [4,6,10,16].…”

Modeling of the Long-Term Epidemic Dynamics of COVID-19 in the United States

“…As mentioned before, many non-pharmaceutical interventions like mask-wearing, social distancing, prohibition of gathering, and school closure, have been enforced to control the spread of COVID-19. Therefore, with the development of the COVID-19 epidemic, the basic reproduction number is expected to gradually reduce due to the increasing number of preventive measures implemented over the course of the epidemic [ 37 , 38 , 39 ]. As such, the basic reproduction number will be time-dependent and should be represented by a dynamic value, , which is defined as the average number of secondary infectious individuals generated by one infectious individual at time t .…”