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This paper aims to explore the behavior of malware propagation on mobile wireless sensor networks (MWSNs). A new malware propagation model with nonlinear incidence rate and sigmoid type removal rate is established, and its global stability, spatiotemporal stability, and optimal control are analyzed. Specifically, the theoretical analysis shows that (i) a forward transcritical bifurcation occurs when the basic reproduction number R 0 > 1 ; (ii) time and space affect the spreading behavior of malware due to spatial distribution; (iii) the optimization technology can effectively control the malware spreading on MWSNs. Finally, some numerical simulations are performed to verify the obtained theoretical results, and the experimental results confirm that the generated patterns are consistent with the field observations of actual MWSNs. Our study helps in controlling the propagation of malware and applicable to design and prediction of the security and robustness of a sensor network. • A new malware propagation model with nonlinear incidence rate and sigmoid type removal rate is studied. • Global stability, spatiotemporal stability, and optimal control are analyzed. • Optimal control technique is employed to reduce the malware propagation. • Stability switching phenomena are obtained via Hopf bifurcation. • Spatio-temporal dynamics depends on transmission rate, time movement of nodes and its initial deployment. [ABSTRACT FROM AUTHOR]