Cristobal Vargas

Analysis of a dengue disease transmission model

A model for the transmission of dengue fever in a constant human population and variable vector population is discussed. A complete global analysis is given, which uses the results of the theory of competitive systems and stability of periodic orbits, to establish the global stability of the endemic equilibrium. The control measures of the vector population are discussed in terms of the threshold condition, which governs the existence and stability of the endemic equilibrium.

Influence of vertical and mechanical transmission on the dynamics of dengue disease

We formulate a non-linear system of differential equations that models the dynamics of transmission of dengue fever. We consider vertical and mechanical transmission in the vector population, and study the effects that they have on the dynamics of the disease. A qualitative analysis as well as some numerical examples are given for the model.

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.

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.

A nonlinear elliptic problem at resonance with a nonsimple eigenvalue

where ;Z IRN is an open and bounded domain with smooth boundary, A , is a nonsimple eigenvalue of A , g is a real valued function and h E Lm(f2). After the 1 9 7 0 paper of Landesman and Lazer [ I ] , the problem has been intensively researched in several directions. For the case in which A , is a simple eigenvalue see [ 2 2 1 1 , and the references therein. For the case in which A , is nonsimple see [ 6 , 2 2 2 5 ] and the references therein. It is common in the literature to distinguish the following situations: ( I ) g ( t ) -+ a , as t + f a with ( a , , a _ ) # ( 0 , O ) . This is the Landesman-Lazer case; ( 2 ) g ( t ) -+ 0 as It1 + a and

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

A continuation method to study periodic orbits of the Froeschlé map

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