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Abstract. Incomplete treatment of patients with infectious tuberculosis (TB) may not only lead to relapse but also to the development of antibiotic resistant TB -one of the most serious health problems facing society today. In this article, we formulate one-strain and two-strain TB models to determine possible mechanisms that may allow for the survival and spread of naturally resistant strains of TB as well as antibiotic-generated resistant strains of TB. Analysis of our models shows that non-antibiotic co-existence is possible but rare for naturally resistant strains while co-existence is almost the rule for strains that result from the lack of compliance with antibiotic treatment by TB infected individuals.

In this work we study a system of differential equations that models the population dynamics of an SIR vector transmitted disease with two pathogen strains. This model arose from our study of the population dynamics of dengue fever. The dengue virus presents four serotypes each of which induces host immunity but only certain degree of crossimmunity to the other different serotypes. The model studied here has been constructed as a paradigm for the study of the epidemiological trends in the disease and for the theoretical study of conditions that permit coexistence in competing strains. Dengue is mainly an epidemic disease in the Americas and this model is geared to generalize this type of dynamics. In the model two different strains of virus are considered with temporary cross-immunity. The model shows the existence of an unstable endemic state ('saddle' point). The nature of this equilibrium produces a transient behavior characterized as a quasi-steady state of long duration during which both dengue serotypes co-circulate. Conditions for asymptotic stability of the equilibria are discussed together with numerical simulations. We argue that the existence of competitive exclusion in this system is due to the interplay between the host superinfection process and the frequency-dependent (vector to host) contact rates.