Gustavo Cruz-Pacheco

Control measures for Chagas disease

Chagas disease, also known as American trypanosomiasis, is a potentially life-threatening illness caused by the protozoan parasite, Trypanosoma cruzi. The main mode of transmission of this disease in endemic areas is through an insect vector called triatomine bug. Triatomines become infected with T. cruzi by feeding blood of an infected person or animal. Chagas disease is considered the most important vector borne infection in Latin America. It is estimated that between 16 and 18 millions of persons are infected with T. cruzi, and at least 20,000 deaths each year. In this work we formulate a model for the transmission of this infection among humans, vectors and domestic mammals. Our main objective is to assess the effectiveness of Chagas disease control measures. For this, we do sensitivity analysis of the basic reproductive number R₀ and the endemic proportions with respect to epidemiological and demographic parameters.

Seasonality and Outbreaks in West Nile Virus Infection

In this paper we analyze the impact of seasonal variations on the dynamics of West Nile Virus infection. We are interested in the generation of new epidemic peaks starting from an endemic state. In many cases, the oscillations generated by seasonality in the dynamics of the infection are too small to be observable. The interplay of this seasonality with the epidemic oscillations can generate new outbreaks starting from the endemic state through a mechanism of parametric resonance. Using experimental data we present specific cases where this phenomenon is numerically observed.

Evolution of two-dimensional lump nanosolitons for the Zakharov-Kuznetsov and electromigration equations

The evolution of lump solutions for the Zakharov-Kuznetsov equation and the surface electromigration equation, which describes mass transport along the surface of nanoconductors, is studied. Approximate equations are developed for these equations, these approximate equations including the important effect of the dispersive radiation shed by the lumps as they evolve. The approximate equations show that lump-like initial conditions evolve into lump soliton solutions for both the Zakharov-Kuznetsov equation and the surface electromigration equations. Solutions of the approximate equations, within their range of applicability, are found to be in good agreement with full numerical solutions of the governing equations. The asymptotic and numerical results predict that localized disturbances will always evolve into nanosolitons. Finally, it is found that dispersive radiation plays a more dominant role in the evolution of lumps for the electromigration equations than for the Zakharov-Kuznetsov equation.

Quantum collapse of a small dust shell

The full quantum mechanical collapse of a small relativistic dust shell is studied analytically, asymptotically and numerically starting from the exact finite dimensional classical reduced Hamiltonian recently derived by Hajicek and Kuchar ˇ. The formulation of the quantum mechanics encounters two problems. The first is the multivalued nature of the Hamiltonian and the second is the construction of an appropriate self-adjoint mo- mentum operator in the space of the shell motion which is confined to a half-line. The first problem is solved by identifying and neglecting orbits of small action in order to obtain a single valued Hamiltonian. The second problem is solved by introducing an appropriate lapse function. The resulting quantum mechanics is then studied by means of analytical and numerical techniques. We find that the region of total collapse has a very small probability. We also find that the solution concentrates around the classical Schwarzschild radius. The present work obtains from first principles a quantum mechanics for the shell and provides numerical solutions, whose behavior is explained by a detailed WKB analysis for a wide class of collapsing shells.

Multi-species interactions in West Nile virus infection

In this paper, we analyse the interaction of different species of birds and mosquitoes on the dynamics of West Nile virus (WNV) infection. We study the different transmission efficiencies of the vectors and birds and the impact on the possible outbreaks. We show that the basic reproductive number is the weighted mean of the basic reproductive number of each species, weighted by the relative abundance of its population in the location. These results suggest a possible explanation of why there are no outbreaks of WNV in Mexico.

Approximate evolution of lump initial conditions for the Benjamin-Ono equation

Abstract In this paper it is shown how the approximate evolution of soliton forming initial conditions for the Benjamin-Ono equation can be described completely in terms of an integrable two-dimensional phase-plane system. It is found that there is good agreement between these approximate solutions and full numerical solutions of the Benjamin-Ono equation, both in the temporal evolution of the soliton amplitude and in the final soliton state for a wide range of initial conditions.

Fast jitter traveling wave solutions in a soliton communication line system with dispersion management

We derive traveling wave solutions for a communication system line with dispersion management using a pertnrbative approach. Use of conservation laws then show that a fast jitter happens when an initial frequency correction is included. @ 1997 Published by Elsevier Science B.V.

A Mathematical Model for the Dynamics of West Nile Virus

Abstract In this paper a mathematical model is formulated to study the dynamics of West Nile Virus (WNV) infection between mosquito and bird population. A qualitative analysis as well as some numerical examples are given for the model.

Vaccination Strategies for SIR Vector-Transmitted Diseases

Vector-borne diseases are one of the major public health problems in the world with the fastest spreading rate. Control measures have been focused on vector control, with poor results in most cases. Vaccines should help to reduce the diseases incidence, but vaccination strategies should also be defined. In this work, we propose a vector-transmitted SIR disease model with age-structured population subject to a vaccination program. We find an expression for the age-dependent basic reproductive number