Optimal harvesting and complex dynamics in a delayed eco-epidemiological model with weak Allee effects

Modelling and bifurcation analysis in a hybrid bioeconomic system with gestation delay and additive Allee effect

“…Remark 1.1 Recently, it has been shown that commercial harvesting on a prey-predator system with Allee effect has a strong impact on population dynamics (see [7,10,[15][16][17][18][19] and the references therein). However, dynamical behavior due to variation of economic interest of commercial harvesting is not discussed in [7,10,[15][16][17][18]. Only dynamic effects of strong Allee effect on population dynamics are considered in [19], the weak Allee effect case is not investigated in [19].…”

Dynamics analysis of a predator–prey system with harvesting prey and disease in prey species

“…Generally speaking, prey-predator models could be divided into three cases by the infective disease in population. The first one is that there is only the infected prey in models (see [3][4][5][6][7]14,19,23,34,45]). Johri et al [19] studied a Lotka-Volterra type predator-prey model with disease in prey and without harvesting, and assumed that the conversion rate of the susceptible prey is the same to that of the infected prey.…”

“…For instance, in an Irish sea, at least four populations of skate and shark have been exploited to extinction [2]. Naturally, optimal harvesting policy is very much needed for such system (see [1,[4][5][6]8,9,18,23,25,28] and references therein). Biswas et al [4] studied an eco-epidemiological system with weak Allee effect and harvesting in prey population, and found that optimal harvesting policy is dependent on both gestation delay and Allee effect.…”

“…Naturally, optimal harvesting policy is very much needed for such system (see [1,[4][5][6]8,9,18,23,25,28] and references therein). Biswas et al [4] studied an eco-epidemiological system with weak Allee effect and harvesting in prey population, and found that optimal harvesting policy is dependent on both gestation delay and Allee effect. Chattopadhy et al [6] investigated a harvesting predator-prey model with infection in the prey population and concluded that harvesting on infected prey prevents the limit cycle oscillations.…”

“…In our model, the predator not only captures the infective prey but also catches the susceptible prey based on the work of Biswas et al [4]. Due to incubation period of infectious disease [14,44], we will consider the affection of time delay in our model.…”