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In this paper, the parameter identification problem of the lateral flow immunoassay (LFIA) devices is investigated via a new switching delayed particle swarm optimization (SDPSO) algorithm. By evaluating an evolutionary factor in each generation, the velocity of the particle can adaptively adjust the model according to a Markov chain in the proposed SDPSO method. During the iteration process, the SDPSO can adaptively select the inertia weight, acceleration coefficients, locally best particle pbest and globally best particle gbest in the swarm. It is worth highlighting that the pbest and the gbest can be randomly selected from the corresponding values in the previous iteration. That is, the delayed information of the pbest and the gbest can be exploited to update the particle's velocity in current iteration according to the evolutionary states. The strategy can not only improve the global search but also enhance the possibility of eventually reaching the gbest. The superiority of the proposed SDPSO is evaluated on a series of unimodal and multimodal benchmark functions. Results demonstrate that the novel SDPSO algorithm outperforms some well-known PSO algorithms in aspects of global search and efficiency of convergence. Finally, the novel SDPSO is successfully exploited to estimate the unknown time-delay parameters of a class of nonlinear state-space LFIA model.