Competitive exclusion in a vector-host model for the dengue fever

Abstract

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.

The role of adaptations in two-strain competition for sylvaticTrypanosoma cruzitransmission

“…which can be shown to exhibit competitive exclusion, similar to other previously studied models for competing pathogen strains with cross-immunity [3,16]. Examination of the steady-state conditions shows system (7) to have three equilibria: the disease-free equilibrium E 0 (0, 0, 0, 0), the equilibrium in which only strain 1 is endemic E 1 (i * h1 N h , 0, i * v1 N v , 0), and the equilibrium in which only strain 2 is endemic,…”

A multispecies model for the transmission and control of mastitis in dairy cows

“…Because the major pathogen infections can cause clinical illness, it is desirable to maintain a parameter set, or impose a control that results in the competitive exclusion of major pathogen infections. Although derived from equations describing a different mechanism for crossprotection between interacting species, the shape of the resulting graph is very similar to those produced from other modelling work related to the competition between strains or species of pathogens [3,11,12].…”

“…3) that has a similar form to those produced from other multistrain\species models [3,11,12]. A similar analysis on the model equations extended to include various control procedures has given some theoretical insight into their possible effects.…”

Sex, Mosquitoes and Epidemics: An Evaluation of Zika Disease Dynamics

“…We assign values to the parameters of the model, considering that ZIKV behaves similarly to dengue fever, e.g., (Adams and Boots 2010;Chowell et al 2007;Feng and Velasco-Hernndez 1996;Pinho et al 2010). To evaluate the sexual transmission effect on the disease spread,we show simulations for different values of φ.…”