Coarse-grained bifurcation analysis and detection of criticalities of an individual-based epidemiological network model with infection control

Implicit Methods for Equation-Free Analysis: Convergence Results and Analysis of Emergent Waves in Microscopic Traffic Models

“…A parameter value of p = 1 introduces a systematic bias into our lifting such that we can vary p gradually to investigate how our results depend on our choice of lifting. For p = 1, the lifting L p,ũ violates the common assumption of equation-free computations, where the identity R • L = I is claimed to be necessary [33,26,21,27,36]. An application of L p,ũ and R without any time evolution in between, yields R(L p,ũ (σ)) = p · σ.…”

“…Thus, the explicit map Φ explicit (t; ·) can be a valid approximation for the flow on the slow manifold in any coordinates only if R • g 0 • L equals the identity on R d . Often this requirement is approximated by R • L = I, because g 0 is in general unknown [21,26,27,33,36]. Note that there is no ε-or t dependence in the limiting map R • g 0 • L, resulting in the much more restrictive condition R • g 0 • L = I than transversality Assumption 2 on R and L. Moreover, R • g 0 • L = I is only a consistency condition, making it possible for Φ explicit (t; ·) to resemble the map of a slow flow.…”

“…Equation-free methods are particularly appealing if either explicit macroscopic descriptions are unavailable, or one wants to study the underlying system near the boundary of validity of its macroscopic description (for example, as one decreases the number of particles, finite size effects may start to appear as small corrections to the macroscopic model). Equation-free analysis has been applied for a large class of multiscale models that roughly fit the description of singularly perturbed systems [9] in a broad sense (see motivation in [24]), such as stochastic systems [28,37], agent-based models [5,6,14], molecular dynamics [4] or neural dynamics [26,33], to perform high-level tasks such as bifurcation analysis, optimization or control design [8,36].…”

Consequences of delays and imperfect implementation of isolation in epidemic control

“…Detrimental effects of delay were also reported during the SARS outbreak, which became more effectively controlled only when the time between onset of symptoms and isolation was shortened [13,16]. Though recent studies have used linear analysis [6,16] and simulations [9] to investigate the role of isolation, a general comprehensive theory of isolation as a means of epidemic control that focuses on consequences of imperfect implementation is lacking, as are studies of the nonlinear effects of isolation protocols. This paper addresses fundamental issues pertaining to imperfections in the implementation of isolation strategies as a means of disease control.…”

A Filippov system describing media effects on the spread of infectious diseases

“…The main characteristic of a Filippov system is that control is suppressed when the value of the threshold function is below a previously chosen threshold policy; above the threshold, control is applied, while in classical systems, control has been implemented all along [13][14][15]. In the following, we call Filippov system (4) defined in region G 1 system S 1 and that defined in region G 2 system S 2 .…”