A two species competition model under the simultaneous effect of toxicant and disease

Asymptotic Behavior of a Stochastic Two‐Species Competition Model under the Effect of Disease

“…rom [4], it follows that the interior equilibrium̂= (̂,̂1,̂2) of deterministic model (2) is feasible when > , ( + ) >̂, > ( 1 + 3 ), and ( − )( + −̂) > 2 . Moreover, from Theorem 3.2 in [4], if there exist positive constants 1 and 2 such that…”

“…There is an extensive literature concerned with model (1) and related deterministic models (see [1][2][3] and the references therein) and we here do not mention them in detail. As mentioned in [4], another major problem in today's modern society is the spread of infectious diseases. A detailed account of modeling and the study of epidemic diseases can be found in the literature [5,6].…”

“…In [8], the authors studied the dynamics of two competing species when one of them is subject to a disease. In [4], the authors assumed that ( ) and ( ) are competing for the same resource and assumed that the disease spreads only in one of the competing species, denoted by ( ). They specified the healthy individuals ( ), the healthy individuals 1 ( ), and the infected individuals of the latter species denoted by 2 ( ).…”

“…∈ R 3 : > 0, > 0, > 0}. From [4], we know that all solutions of model (2) will lie in the region 1 = {( , 1 , 2 ) ∈ R 3 + : 0 ≤ ≤ , 0 ≤ 1 ≤ , 0…”

Modeling and Analysis of a Single Species Population with Viral Infection in Polluted Environment

“…As a result ecologists acknowledge the importance of disease and parasite in the dynamics of the population [15][16][17][18][19]. Recently few interesting mathematical models with combined effects of disease and toxicant were studied [20][21][22], for competing and prey predator dynamics. Keeping in view of the above, in this paper, we have proposed a mathematical model by considering the combined effect of both the infection and the toxicant through food intake and environmental toxicant.…”