Sourav Kumar Sasmal

A delayed eco-epidemiological system with infected prey and predator subject to the weak Allee effect

We consider a system of delay differential equations to represent predator-prey eco-epidemic dynamics with weak Allee effect in the growth of predator population. The basic aim of the paper is to observe the dynamics of such system under the influence of gestation delay of predator and Allee parameter. We analyze essential mathematical features of the proposed model such as uniform persistence, stability and Hopf-bifurcation at the interior equilibrium point of the system. Global asymptotic stability analysis of the positive equilibrium points by constructing a suitable Lyapunov function for the delayed model is carried out separately. We perform several numerical simulations to illustrate the applicability of the proposed mathematical model and our analytical findings. We observe that the system exhibits chaotic oscillation due to increase of the delay parameter τ. We also observe that there is a threshold of Allee parameter above which the predator population will be washed away from the system.

A host–parasitoid system with predation-driven component Allee effects in host population

Allee effects and parasitism are common biological phenomena observed in nature, which are believed to have significant impacts in ecological conservation programmes. In this article, we investigate population dynamics of a discrete-time host–parasitoid system with component Allee effects induced by predation satiation in host to study the synergy effects of Allee effects and parasitism. Our model assumes that parasitism attacks the host after the density dependence of the host. The interactions of component Allee effects and parasitism can lead to extremely rich dynamics that include but are not limited to extinction of both species due to Allee effects at their low population density, multiple attractors, strange interior attractors and even crisis of strange attractor due to high parasitism. We perform local and global analysis to study the number of equilibria and their stability; and study the extinction and permanence of our host–parasitoid system. One of the most interesting results shows that the combination of strong Allee effects and parasitism may promote the coexistence of both host and parasite at their high population density. In addition, component Allee effects may destroy interior equilibrium under different values of parameters’ ranges.

Estimating dengue type reproduction numbers for two provinces of Sri Lanka during the period 2013-14.

Dengue is an endemic disease in the southeast Asian country Sri Lanka. Two seasonal peaks of dengue incidence were observed every year since 2002 onwards. In this study, we formulate a 2-strain dengue model for analyzing the monthly seasonal dengue incidence data from 2 provinces of Sri Lanka during the period April 2013 to September 2014. The seasonality is incorporated in the model in terms of mosquito biting rate, which we assume to be time periodic. We estimated 2 primary reproduction numbers and the basic reproduction number in a periodic environment using dengue incidence data from the western and the central provinces of Sri Lanka. We also estimated different time-average type reproduction numbers from the model using the data from these 2 provinces. Using univariate sensitivity analysis, we measured the sensitivity of the time average reproduction number ( ) When we vary different parameters of the proposed dengue model, we find the transmission probability of human susceptibility to strain-I infection and the mosquito mortality rate parameters are the most sensitive parameters in dengue transmission in these 2 provinces.

Intra-specific competition in predator can promote the coexistence of an eco-epidemiological model with strong Allee effects in prey.

An eco-epidemiological model with Allee effects and disease in prey has been proposed and analyzed. The proposed model incorporates intra-specific competition in predator due to the limited food source, and assumes standard incidence disease transmission. We analyzed the corresponding submodels with and without the Allee effects to obtain the complete dynamics of the full model. Our results show that our full model shows multi-stability between the planner equilibriums (where the susceptible prey co-exists with infected prey or predator); both the full model and its submodels exhibit the hydra effects caused by the intra-specific competition in predator. We determined the existence of multiple interior attractors and their stability. Our analysis shows that our system has at most two interior equilibria whose stability is either both saddle or one stable with another one saddle. One of the most interesting findings is that the competition in the predator can promote the coexistence of all the three populations. In addition, we discussed how the frequency-dependent transmission differs from the model with the density-dependent transmission and compare the hydra effects observed in our model to other existing models in literature.

Effect of dispersal in two-patch prey–predator system with positive density dependence growth of preys

Prey-predator systems in patchy environment, connected through dispersal between patches is a very common phenomenon observed in nature, which have a significant impact in ecology, species persistence and extinction, etc. In the present paper, we consider a two patch prey-predator system where the patches are connected through dispersal between preys populations only. We consider positive density dependence growth for preys population. In addition, we consider the time scale difference (different life span) between preys and predator populations. From our study, we can conclude that dispersal can save both the populations from extinction, when in a single patch initial preys density is lower the Allee threshold. Also, time difference can increase the basin of attraction of the coexistence equilibrium of our two-patch model. Time scale difference also can help to reach the steady state faster than the without time scale difference, and it also causes the amplitude death when populations are in limit cycle oscillation. We also analyze our model by considering the time delay in dispersal dynamics, and we show that delay induced dispersal can stabilize the system and cause the amplitude death when individual populations are in the limit cycle, without dispersal. In addition, dispersal in non-identical patches can stabilize at its interior equilibrium even if the environment is harsh for both the populations in both the individual patches.

Survivability of a metapopulation under local extinctions

A metapopulation structure in landscape ecology comprises a group of interacting spatially separated subpopulations or patches of the same species that may experience several local extinctions. This makes the investigation of survivability (in the form of global oscillation) of a metapopulation on top of diverse dispersal topologies extremely crucial. However, among various dispersal topologies in ecological networks, which one can provide higher metapopulation survivability under local extinction is still not well explored. In this article, we scrutinize the robustness of an ecological network consisting of prey-predator patches having Holling type I functional response, against progressively extinct population patches. We present a comprehensive study on this while considering global, small-world, and scale-free dispersal of the subpopulations. Furthermore, we extend our work in enhancing survivability in the form of sustained global oscillation by introducing asymmetries in the dispersal rates of the considered species. Our findings affirm that the asynchrony among the patches plays an important role in the survivability of a metapopulation. In order to demonstrate the model independence of the observed phenomenon, we perform a similar analysis for patches exhibiting Holling type II functional response. On the grounds of the obtained results, our work is expected to provide a better perception of the influence of dispersal arrangements on the global survivability of ecological networks.

A PREDATOR-PEST MODEL WITH ALLEE EFFECT AND PEST CULLING AND ADDITIONAL FOOD PROVISION TO THE PREDATOR — APPLICATION TO PEST CONTROL

The harmful effects of insect pests on human health and agricultural output are a major global concern. Frequent use of chemical pesticides as a means of pest control can have detrimental effects on the environment, resulting in water and soil pollution, food toxicity, resistance to pesticides, etc. As a result, there is an urgent need to develop a biological pest-control approach that would mitigate these harmful effects. The main purpose of the present study is to explore the interaction between strong Allee effects in the pest with other biological control mechanisms, such as providing additional food to the predator and pest culling as a means of proposing an efficient pest-control policy. To achieve this goal, local stability analysis around the equilibria, possible bifurcation and some basic dynamical features of the system was performed. Our work focuses on the basin of stability in multiple stable regions of the model, which yields the probability of convergence of each equilibrium for a given set of different initial conditions. The system exhibits bi-stability and tri-stability of the equilibria. Our findings indicate that providing additional food to the predator can be an efficient stand-alone pest control strategy, which can, if needed, be combined with other methods.

A two-patch prey-predator model with predator dispersal driven by the predation strength

Foraging movements of predator play an important role in population dynamics of prey-predator systems, which have been considered as mechanisms that contribute to spatial self-organization of prey and predator. In nature, there are many examples of prey-predator interactions where prey is immobile while predator disperses between patches non-randomly through different factors such as stimuli following the encounter of a prey. In this work, we formulate a Rosenzweig-MacArthur prey-predator two patch model with mobility only in predator and the assumption that predators move towards patches with more concentrated prey-predator interactions. We provide completed local and global analysis of our model. Our analytical results combined with bifurcation diagrams suggest that: (1) dispersal may stabilize or destabilize the coupled system; (2) dispersal may generate multiple interior equilibria that lead to rich bistable dynamics or may destroy interior equilibria that lead to the extinction of predator in one patch or both patches; (3) Under certain conditions, the large dispersal can promote the permanence of the system. In addition, we compare the dynamics of our model to the classic two patch model to obtain a better understanding how different dispersal strategies may have different impacts on the dynamics and spatial patterns.

Mathematical modeling on T-cell mediated adaptive immunity in primary dengue infections

At present, dengue is the most common mosquito-borne viral disease in the world, and the global dengue incidence is increasing day by day due to climate changing. Here, we present a mathematical model of dengue viruses (DENVs) dynamics in micro-environment (cellular level) consisting of healthy cells, infected cells, virus particles and T-cell mediated adaptive immunity. We have considered the explicit role of cytokines and antibody in our model. We find that the virus load goes down to zero within 6 days as it is common for DENV infection. From our analysis, we have identified the important model parameters and done the numerical simulation with respect to such important parameters. We have shown that the cytokine mediated virus clearance plays a very important role in dengue dynamics. It can change the dynamical behavior of the system and causes essential extinction of the virus. Finally, we have incorporated the antiviral treatment for dengue in our model and shown that the basic reproduction number is directly proportional to the antiviral treatment effects.

Effect of diseases on symbiotic systems

There are many species living in symbiotic communities. In this study, we analyzed models in which populations are in the mutualism symbiotic relations subject to a disease spreading among one of the species. The main goal is the characterization of symbiotic relations of coexisting species through their mutual influences on their respective carrying capacities, taking into account that this influence can be quite strong. The functional dependence of the carrying capacities reflects the fact that the correlations between populations cannot be realized merely through direct interactions, as in the usual predator-prey Lotka-Volterra model, but also through the influence of each species on the carrying capacities of the other one. Equilibria are analyzed for feasibility and stability, substantiated via numerical simulations, and global sensitivity analysis identifies the important parameters having a significant impact on the model dynamics. The infective growth rate and the disease-related mortality rate may alter the stability behavior of the system. Our results show that introducing a symbiotic species is a plausible way to control the disease in the population.