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Load-balance is one of the most important problems in the multipath routing. To this point, this paper proposed a new bio-inspired adaptive multipath routing (BAMR) protocol based on a mathematic biology model ARAS, which is inspired by the host Escherichia coli cells to regulate its metabolic synthesis to keep the high cell growth rate. The BAMR take the routing decision to imitate the adaptive behavior of biological systems. Firstly, BAMR integrates the round trip delay and the available bandwidth of path for calculating a new bio-inspired routing-decision metric, i.e., the path fitness, which can be equivalently regarded as the growth rate of cell volume. Then the fitness of each path is applied to the ARAS model to calculate its packet delivery gain, respectively, which is equivalent to the concentration of each nutrient in the bacterial cell. Finally, the source node chooses the path with the highest packet delivery gain for each packet. Through the proposed routing protocol, the source node can efficiently distributes traffic among multiple paths, and allocates more traffic to a less loaded path within the path capacity.