An optimal isolation policy for an epidemic

Abstract

Policies of isolating infectives in the general stochastic epidemic are considered. With costs assigned to the infection and isolation of individuals, an optimal policy is found, which at any stage minimises the expected future cost. An optimal policy is also found for the general deterministic epidemic and the two policies are compared. Finally, some numerical examples are provided.

Optimal impulse control of a SIR epidemic

“…We provided the explicit optimal solution to the stated impulse control problem for the SIR epidemic. Similarly to other works, [8][9][10] if the intervention is desirable, then it is optimal to isolate all the infectives instantly in one go. (Note, in the work of Piunovskiy et al, 10 only the total isolations were allowed.)…”

“…Such models, the case of isolation, were investigated in other works. [8][9][10] Roughly speaking, the optimal strategy prescribes to isolate all the infectives at once, as soon as the number of infectives is below a certain threshold.…”

“…Impulse control of various dynamical systems attracts the attention of many researchers, eg, those in other works 8,9,[11][12][13][14][15][16][17][18][19][20][21][22][23][24] to mention the most relevant and the most recent works. The underlying system can be described in terms of ordinary 8,9,[11][12][13]20,[22][23][24] or stochastic 17,21 differential equations. In other works, [14][15][16]19 along with the given deterministic drift, there are spontaneous (or natural) Markov jumps of the state.…”

“…21 The goal is to minimize the total (expected) accumulated cost, which may be discounted 12,[14][15][16]18,19,21 or not. 8,12,13,17,20,22 The popular method of attack to such problems is dynamic programming. 12,[14][15][16]18,19,21,23 In other works, 11,20,22,24 versions of the Pontryagin maximum principle are used.…”

“…In the current paper, we study the modification of the standard Kermack-McKendrick model, 1 suggested in the work of Gleißner. 25 Note that Abakuks 8 and Kyriakidis and Pavitsos 9 considered the standard SIR model. 1 Moreover, the solution was based on partially intuitive and special reasoning, rather than on the general impulse control theory.…”