Structure of optimal control in the model of propagation of two malicious softwares

The security risks incurred by the spread of malware in computer and wireless networks can be reduced by the immunization of nodes, using security and antivirus patches. Malware, which captures personal and corporate confidential data, induces different damages, including costs generated by the necessity to compensate disclosure of private information, loss of money and social damage caused by loss of reputation. The distribution of security and antivirus patches in a network enables the control of the proliferation of malicious software and decreases possible losses. We formulate an optimal control problem for the case whether two different types of malware can circulate at the same time in a computer network and present an optimal strategy of resistance to malvares.