Global stabilizing feedback law for a problem of biological control of mosquito-borne diseases

The control of the spread of dengue fever by introduction of the intracellular parasitic bacterium Wolbachia in populations of the vector Aedes aegypti, is presently one of the most promising tools for eliminating dengue, in the absence of an efficient vaccine. The success of this operation requires locally careful planning to determine the adequate number of mosquitoes carrying the Wolbachia parasite that need to be introduced into the natural population. The latter are expected to eventually replace the Wolbachia-free population and guarantee permanent protection against the transmission of dengue to human. In this paper, we propose and analyze a model describing the fundamental aspects of the competition between mosquitoes carrying Wolbachia and mosquitoes free of the parasite. We then introduce a simple feedback control law to synthesize an introduction protocol, and prove that the population is guaranteed to converge to a stable equilibrium where the totality of mosquitoes carry Wolbachia. The techniques are based on the theory of monotone control systems, as developed after Angeli and Sontag. Due to bistability, the considered input-output system has multivalued static characteristics, but the existing results are unable to prove almost-global stabilization, and ad hoc analysis has to be conducted.

The revenge of the market on the rentiers why neo-liberal reports of the end of history turned out to be premature

Starting from the perspective of heterodox Keynesian-Minskyian-Kindlebergian financial economics, this paper begins by highlighting a number of mechanisms that contributed to the current financial crisis. These include excess liquidity, income polarisation, conflicts between financial and productive capital, lack of intelligent regulation, asymmetric information, principal-agent dilemmas and bounded rationalities. However, the paper then proceeds to argue that perhaps more than ever the ‘macroeconomics’ that led to this crisis only makes analytical sense if examined within the framework of the political settlements and distributional outcomes in which it had operated. Taking the perspective of critical social theories the paper concludes that, ultimately, the current financial crisis is the outcome of something much more systemic, namely an attempt to use neo-liberalism (or, in US terms, neo-conservatism) as a new technology of power to help transform capitalism into a rentiers’ delight. And in particular, into a system without much ‘compulsion’ on big business; i.e., one that imposes only minimal pressures on big agents to engage in competitive struggles in the real economy (while inflicting exactly the opposite fate on workers and small firms). A key component in the effectiveness of this new technology of power was its ability to transform the state into a major facilitator of the ever-increasing rent-seeking practices of oligopolistic capital. The architects of this experiment include some capitalist groups (in particular rentiers from the financial sector as well as capitalists from the ‘mature’ and most polluting industries of the preceding techno-economic paradigm), some political groups, as well as intellectual networks with their allies – including most economists and the ‘new’ left. Although rentiers did succeed in their attempt to get rid of practically all fetters on their greed, in the end the crisis materialised when ‘markets’ took their inevitable revenge on the rentiers by calling their (blatant) bluff.