Given independent multiple access logs, we develop a mathematical model to identify the number of malicious hosts in the current Internet. In our model, the number of malicious hosts is formalized as a function taking two inputs, namely the duration of observation and the number of sensors. Assuming that malicious hosts with statically assigned global addresses perform random port scans to independent sensors uniformly distributed over the address space, our model gives the asymptotic number of malicious source addresses in two ways. Firstly, it gives the cumulative number of unique source addresses in terms of the duration of observation. Secondly, it estimates the cumulative number of unique source addresses in terms of the number of sensors. To evaluate the proposed method, we apply the mathematical model to actual data packets observed by ISDAS distributed sensors over a one-year duration from September 2004, and check the accuracy of identification of the number of malicious hosts.