Impact of temporal correlations on high risk outbreaks of independent and cooperative SIR dynamics

Fractional optimal control strategies for hepatitis B virus infection with cost-effectiveness analysis

Hepatitis B disease is a communicable disease that is caused by the hepatitis B virus and has become a significant health problem in the world. It is a contagious disease that is transmittable from person to person either horizontally or vertically. This current study is aimed at sensitivity analysis and optimal control strategies for a fractional hepatitis B epidemic model with a saturated incidence rate in the sense of the Caputo order fractional derivative approach. Fundamental properties of the proposed fractional order model are obtained and discussed. A detailed analysis of disease-free equilibrium and endemic equilibrium points is given by applying fractional calculus theory, which is a generalized version of classical calculus. Sensitivity indexes are calculated for the classical order model. Illustrative graphics that show the dependence of the sensitivity index on fractional order derivative for [Formula: see text] are provided. Based on the results of the sensitivity analysis and using Pontryagin's Maximum Principle, optimal control strategies for preventing hepatitis B infection with vaccination and treatment are considered. Fractional Euler's method is used to carry out the numerical simulation for the proposed fractional optimal control system and the obtained results are analyzed. The results of the analysis reveal that hepatitis B disease can be prevented if necessary precautionary is taken or effective vaccination and treatment control measures are applied. The analysis of cost-effectiveness is also conducted and discussed.

Directed percolation in random temporal network models with heterogeneities

The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similarly to percolation theory on static networks, this mapping is valid under the approximation that the structure and interaction dynamics of the temporal network are determined by its local properties, and, otherwise, it is maximally random. We challenge these conditions and demonstrate the robustness of this mapping in case of more complicated systems. We systematically analyze random and regular network topologies and heterogeneous link-activation processes driven by bursty renewal or self-exciting processes using numerical simulation and finite-size scaling methods. We find that the critical percolation exponents characterizing the temporal network are not sensitive to many structural and dynamical network heterogeneities, while they recover known scaling exponents characterizing directed percolation on low-dimensional lattices. While it is not possible to demonstrate the validity of this mapping for all temporal network models, our results establish the first batch of evidence supporting the robustness of the scaling relationships in the limited-time reachability of temporal networks.

Social distancing in pedestrian dynamics and its effect on disease spreading

Nonpharmaceutical measures such as social distancing can play an important role in controlling the spread of an epidemic. In this paper, we use a mathematical model combining human mobility and disease spreading. For the mobility dynamics, we design an agent-based model consisting of pedestrian dynamics with a novel type of force to resemble social distancing in crowded sites. For the spreading dynamics, we consider the compartmental susceptible-exposed-infective (SEI) dynamics plus an indirect transmission with the footprints of the infectious pedestrians being the contagion factor. We show that the increase in the intensity of social distancing has a significant effect on the exposure risk. By classifying the population into social distancing abiders and nonabiders, we conclude that the practice of social distancing, even by a minority of potentially infectious agents, results in a drastic change in the population exposure risk, but it reduces the effectiveness of the protocols when practiced by the rest of the population. Furthermore, we observe that for contagions for which the indirect transmission is more significant, the effectiveness of social distancing would be reduced. This study can help to provide a quantitative guideline for policy-making on exposure risk reduction.