Michel Iskin da Silveira Costa

Drug kinetics and drug resistance in optimal chemotherapy

A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. First-order drug kinetics and drug resistance are taken into account in a class of optimal control problems. The results show that the strategy corresponding to the maximum rate of drug injection is optimal for the Malthusian model of cell growth (which is a relatively good model for the initial phase of tumor growth). For more general models of cell growth, this strategy proved to be suboptimal under certain conditions.

Chemotherapeutic treatments involving drug resistance and level of normal cells as a criterion of toxicity

A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. Drug resistance and toxicity conveyed through the level of normal cells are taken into account in a class of optimal control problems. Alternative treatments for the exponential tumor growth are set forth for cases where optimal treatments are not available.

Exploitation of a single species by a threshold management policy.

Continuous time models of single exploited populations usually generate outcomes expressing a dependence of yield and economic items on harvest intensity. In this work it is shown that a known threshold policy is able to generate yield and related economic items that do not depend on harvest intensity, but rather on the values of the population threshold itself and the species intrinsic parameters. It is argued that since this result can be carried over to other models of single species dynamics, it may have significant implications in the management and conservation of exploited populations.

Predator harvesting in stage dependent predation models: insights from a threshold management policy.

Stage dependent predation may give rise to the hydra effect--the increase of predator density at equilibrium as its mortality rate is raised. Management strategies that adjust predator harvest rates or quotas based on responses of populations to past changes in capture rates may eventually lead to a catastrophic collapse of predator species. A proposed threshold management policy avoids the hydra effect and its subsequent danger of predator extinction. Suggestions to extend the application of threshold policies in areas such as intermediate disturbance hypothesis, density-trait mediated interactions and non-optimal anti-predatory behavior are put forward.

Prey dynamics under generalist predator culling in stage structured models

In this paper, by means of mathematical dynamical models we investigate the impacts of predator culling on a prey population structured in two stage classes, juveniles and adults, assuming stage specific predation by two generalist predators with functional responses types 2 and 3 in all possible combinations. According to the chosen set of parameter values, these impacts can manifest through possible demographic Allee effects, sustained population oscillations, alternative stable states (e.g., predator-pit-like behavior) and Hydra effect, which are all discussed, in turn, in terms of species conservation, harvest yield and pest biological control.

Integrated Pest Management in a Predator-Prey System with Allee Effects

A commonly used biocontrol strategy to control invasive pests with Allee effects consists of the deliberate introduction of natural enemies. To enhance the effectiveness of this strategy, several tactics of control of invasive species (e.g., mass-trapping, manual removal of individuals, and pesticide spraying) are combined so as to impair pest outbreaks. This combination of strategies to control pest species dynamics are usually named integrated pest management (IPM). In this work, we devise a predator-prey dynamical model in order to assess the influence of the intensity of chemical killing on the success of an IPM. The biological and mathematical framework presented in this study can also be analyzed in the light of species conservation and food web dynamics theory.

Modeling Trophic Interactions in Insect Population Dynamics

The complexity of insect communities involves a large number of interacting species. Predators may often exploit a wide range of food sources, frequently acting as generalists, omnivores or intraguild predators. In addition to these kinds of interactions, natural communities also contain species with two types of reproductive strategy, known as semelparity and iteroparity. In this chapter, different mathematical models representing trophic interactions will be considered, assuming both types of life history, in the framework of insect population dynamics and biocontrol. The results show that among other factors the interaction strength of the species involved plays an important role in the determination of the food web dynamics.

Chemotherapeutic Treatments with Time Increasing Mutation Rate to Drug Resistance

A system of differential equations for the control of tumor growth cells in a cycle nonspecific chemotherapy is analyzed. Spontaneously acquired drug resistance is taken into account by means of a mutation rate increasingly dependent on time. For general tumor growth and drug kill rates the optimal treatment consists of maximum allowable drug concentration throughout, supporting the conjecture that variable mutation rate to drug resistance does not basically alter the corresponding results of constant mutation rate.