Sudip Samanta

Effect of awareness programs by media on the epidemic outbreaks: A mathematical model

We propose and analyze a mathematical model to assess the effect of awareness programs by media on the prevalence of infectious diseases. Such programs may induce behavioral changes in the population, and divide the susceptible class into two subclasses with different infectivity rates. The biologically feasible equilibria and their stability properties are analyzed and discussed. The model analysis reveals that the rate of executing awareness programs has a substantial effect over the system and sustained oscillation may arise with increasing its value above a threshold. This threshold poses a challenge to control the epidemic. Numerical simulation also supports the analytical findings.

Awareness programs control infectious disease - Multiple delay induced mathematical model

We study the effect of awareness programs on the spreading of infectious disease.Awareness divides the susceptible class into two subclasses: aware and unaware.An SIS epidemic model with awareness and multiple delays has been studied.Local stability, bifurcation analysis and realistic simulations have been performed.An awareness program has a significant effect on disease control. We propose and analyze a mathematical model to study the impact of awareness programs on an infectious disease outbreak. These programs induce behavioral changes in the population, which divide the susceptible class into two subclasses, aware susceptible and unaware susceptible. The system can have a disease-free equilibrium and an endemic equilibrium. The expression of the basic reproduction number and the conditions for the stability of the equilibria are derived. We further improve and study the model by introducing two time-delay factors, one for the time lag in memory fading of aware people and one for the delay between cases of disease occurring and mounting awareness programs. The delayed system has positive bounded solutions. We study various cases for the time delays and show that in general the system develops limit cycle oscillation through a Hopf bifurcation for increasing time delays. We show that under certain conditions on the parameters, the system is permanent. To verify our analytical findings, the numerical simulations on the model, using realistic parameters for Pneumococcus are performed.

Cannibalistic Predator–Prey Model with Disease in Predator — A Delay Model

In this paper, we propose and analyze a cannibalistic predator–prey model with a transmissible disease in the predator population. The disease can be transmitted through contacts with infected individuals as well as the cannibalism of an infected predator. We also consider incubation delay in disease transmission, where the incubation period represents the time in which the infectious agent develops in the host. Local stability analysis of the system around the biologically feasible equilibria is studied. Bifurcation analysis of the system around interior equilibrium is also studied. Applying the normal form theory and central manifold theorem, the direction of Hopf bifurcation, the stability and the period of bifurcating periodic solutions are derived. Under appropriate conditions, the permanence of the system with time delay is proved. Our results suggest that incubation delay destabilizes the system and can produce chaos. We also observe that cannibalism can control disease and population oscillations. Extensive numerical simulations are performed to support our analytical results.

Effect of awareness program in disease outbreak – A slow–fast dynamics

Abstract The interplay between the impact of awareness and the disease outbreak through network epidemic models and non-network epidemic models have recently received considerable attention to the researchers. The present study falls under the non-network epidemic models. Human awareness results in the reduction of susceptibility to infection, naturally, in the epidemiological study this factor should be included. The demographic and epidemic processes are comparatively slow in compared with the awareness. In this work, we investigate the effect of awareness program in disease outbreak – a slow fast dynamics with an SIS (susceptible-infected-susceptible) model. We assume that susceptible individual switches between aware and unaware states very fast, whereas the disease transmission and other biological processes are comparatively slow. Our theoretical and numerical simulation results suggest that increase in switching ratio and lower infectivity among aware susceptible population drastically reduce the disease prevalence. We believe this finding may be useful in disease control programs.

Mathematical modeling of cascading migration in a tri-trophic food-chain system.

Diel vertical migration is a behavioral antipredator defense that is shaped by a trade-off between higher predation risk in surface waters and reduced growth in deeper waters. The strength of migration of zooplankton increases with a rise in the abundance of predators and their exudates (kairomone). Recent studies span multiple trophic levels, which lead to the concept of coupled vertical migration. The migrations that occur at one trophic level can affect the vertical migration of the next lower trophic level, and so on, throughout the food chain. This is called cascading migration. In this paper, we introduce cascading migration in a well-known model (Hastings and Powell, Ecology 73:896–903, 1991). We represent the dynamics of the system as proposed by Hastings and Powell as a phytoplankton–zooplankton–fish (prey–middle predator–top predator) model where fish affect the migrations of zooplankton, which in turn affect the migrations of motile phytoplankton. The system under cascading migration enhances system stability and population coexistence. It is also observed that for a higher rate of cascading migration, the system shows chaotic behavior. We conclude that the observations of Hastings and Powell remain true if the cascading migration rate is high enough.

EFFECT OF KAIROMONE ON PREDATOR–PREY DYNAMICS — A DELAY MODEL

In most of the predator–prey systems, prey individuals make transitions between vulnerable and invulnerable states or locations. This transition is regulated by various inducible defense mechanisms. Diel vertical migration (DVM) in zooplankton is the most effective and instantaneous defense observed in zooplankton population. Zooplankton shows downward vertical migration in the daytime in the presence of predators (or predator kairomones) to avoid predation (i.e. refuge use), and it enters into the surface water again at night to graze phytoplankton. The dynamics of the planktonic ecosystem under DVM of zooplankton along with fish kairomone and the multiple delays due to migration for vulnerable and invulnerable prey and reproduction in the predator population is of considerable interest both in theoretical and experimental ecologists. By developing mathematical model, we analyze such a system. The conditions for which the system enters into Hopf-bifurcation are obtained. Moreover, the conditions for which the bifurcating branches are supercritical are also derived. Our results indicate that DVM along with the effect of kairomone and multiple delays with a certain range are responsible to enhance the stability of the system around the positive interior equilibrium point.

CONTROL OF DISEASE IN PREY POPULATION BY SUPPLYING ALTERNATIVE FOOD TO PREDATOR

A simple predator–prey system with disease in prey population and alternative food for the predator is proposed and analyzed. The main objective of the present investigation is to observe the conditions for which the disease in prey population will be controlled. It is observed that supply of alternative food to the predator population can make the system disease free. Enrichment also plays an important role in suppressing the infected population in the presence of alternative food. However, in the absence of predator population, enrichment increases the disease prevalence instead of reducing it. We finally conclude that supply of alternative food to the predator provides a healthy disease free system.

Chaos control via feeding switching in an omnivory system.

Tanabe and Namba (Ecology, 86, 3411-3414) studied a three species Lotka-Volterra model with omnivory and explored that omnivory can create chaos. It is well documented that predator switching is a similar biological phenomenon to omnivory and likely to occur simultaneously. In the present paper, the tri-trophic Lotka-Volterra food web model with omnivory and predator switching is re-investigated. We observe that if we incorporate predator switching in the system and the intensity of predator switching increases above a threshold value, then the system will be stable from chaotic dynamics. To study the global dynamics of the system extensive numerical simulations are performed. Our analytical and numerical results suggest that predator switching mechanism enhances the stability and the persistence of a food chain system.

THE ROLE OF ADDITIONAL FOOD IN A PREDATOR–PREY MODEL WITH A PREY REFUGE

In this paper, we propose and analyze a predator–prey model with a prey refuge and additional food for predators. We study the impact of a prey refuge on the stability dynamics, when a constant proportion or a constant number of prey moves to the refuge area. The system dynamics are studied using both analytical and numerical techniques. We observe that the prey refuge can replace the predator–prey oscillations by a stable equilibrium if the refuge size crosses a threshold value. It is also observed that, if the refuge size is very high, then the extinction of the predator population is certain. Further, we observe that enhancement of additional food for predators prevents the extinction of the predator and also replaces the stable limit cycle with a stable equilibrium. Our results suggest that additional food for the predators enhances the stability and persistence of the system. Extensive numerical experiments are performed to illustrate our analytical findings.

The effect of nanoparticles on plankton dynamics: a mathematical model.

A simple modification of the Rosenzweig-MacArthur predator (zooplankton)-prey (phytoplankton) model with the interference of the predators by adding the effect of nanoparticles is proposed and analyzed. It is assumed that the effect of these particles has a potential to reduce the maximum physiological per-capita growth rate of the prey. The dynamics of nanoparticles is assumed to follow a simple Lotka-Volterra uptake term. Our study suggests that nanoparticle induce growth suppression of phytoplankton population can destabilize the system which leads to limit cycle oscillation. We also observe that if the contact rate of nanoparticles and phytoplankton increases, then the equilibrium densities of phytoplankton as well as zooplankton decrease. Furthermore, we observe that the depletion/removal of nanoparticles from the aquatic system plays a crucial role for the stable coexistence of both populations. Our investigation with various types of functional response suggests that Beddington functional response is the most appropriate representation of the interaction of phytoplankton-nanoparticles in comparison to other widely used functional responses.