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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.

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SEIR epidemiological models with the inclusion of quarantine and isolation are used to study the control and intervention of infectious diseases. A simple ordinary differential equation (ODE) model that assumes exponential distribution for the latent and infectious stages is shown to be inadequate for assessing disease control strategies. By assuming arbitrarily distributed disease stages, a general integral equation model is developed, of which the simple ODE model is a special case. Analysis of the general model shows that the qualitative disease dynamics are determined by the reproductive number [Formula: see text], which is a function of control measures. The integral equation model is shown to reduce to an ODE model when the disease stages are assumed to have a gamma distribution, which is more realistic than the exponential distribution. Outcomes of these models are compared regarding the effectiveness of various intervention policies. Numerical simulations suggest that models that assume exponential and non-exponential stage distribution assumptions can produce inconsistent predictions.

Treating HIV-infected patients with a combination of several antiretroviral drugs usually contributes to a substantial decline in viral load and an increase in CD4(+) T cells. However, continuing viral replication in the presence of drug therapy can lead to the emergence of drug-resistant virus variants, which subsequently results in incomplete viral suppression and a greater risk of disease progression. In this paper, we use a simple mathematical model to study the mechanism of the emergence of drug resistance during therapy. The model includes two viral strains: wild-type and drug-resistant. The wild-type strain can mutate and become drug-resistant during the process of reverse transcription. The reproductive ratio [Symbol: see text](0) for each strain is obtained and stability results of the steady states are given. We show that drug-resistant virus is more likely to arise when, in the presence of antiretroviral treatment, the reproductive ratios of both strains are close. The wild-type virus can be suppressed even when the reproductive ratio of this strain is greater than 1. A pharmacokinetic model including blood and cell compartments is employed to estimate the drug efficacies of both the wild-type and the drug-resistant strains. We investigate how time-varying drug efficacy (due to the drug dosing schedule and suboptimal adherence) affects the antiviral response, particularly the emergence of drug resistance. Simulation results suggest that perfect adherence to regimen protocol will well suppress the viral load of the wild-type strain while drug-resistant variants develop slowly. However, intermediate levels of adherence may result in the dominance of the drug-resistant virus several months after the initiation of therapy. When more doses of drugs are missed, the failure of suppression of the wild-type virus will be observed, accompanied by a relatively slow increase in the drug-resistant viral load.