Journal of Biological Systems

In this paper, a stochastic nutrient–plankton model with seasonal fluctuation was developed to investigate how seasonality and environmental noise affect the dynamics of aquatic ecosystems. First, the survival analysis of plankton was proposed. Then, by using Lyapunov function and Khasminskii’s theory for periodic Markov processes, we derive the sufficient conditions for the existence of positive periodic solution. The numerical simulations were carried out to provide a better understanding of the model, and the results indicate that seasonal fluctuation is beneficial to the coexistence of plankton species.

In this paper, we propose a new dynamical system model pertaining to Dengue transmission, and investigate its consequent morphology. We present and study various ramifications of our mathematical model for Dengue spread, encapsulated in a spatio-temporal differential system made of reaction–diffusion equations. Diffusion terms are incorporated into the said model by using specific derivations for infected mosquitoes, and infected humans, as well. Moreover, mechanisms for the nearest neighbor(s) infections are integrated into the model. Furthermore, using adaptive multigrid finite difference with decoupling and quasi-linearization techniques, we investigate two main factors for Dengue spatial propagation. We determine the effects of temperature variations, and the mobility of infectious agents, be they mosquitoes or humans. Finally, the proposed model-based analytico-numerical results are obtained, and rendered in graphical profiles, which show the major role the climate temperature and the mobility of infected humans have on the spread and speed of the disease. The consequent proposed model outcomes and health-based ramifications are then raised, discussed, and then validated.

The extinction and the persistence of the population of the harmful sheep blowfly (Lucilia cuprina) are discussed in this paper through a stochastic mathematical model. Using appropriate Lyapunov functionals, the extinction of these flies depends on the time to oviposition and the time between generations. The oviposition period must be sufficiently short. Another species of blowfly, called Lucilia sericata, also attacks sheep in many areas. Both blowflies are ectoparasites of warm-blooded vertebrates, particularly domestic sheep. These two blowflies are related to sharing the same mitochondrial DNA sequences, although the two species are distinct. A sufficiently small egg-laying delay then leads to the rapid extinction of both blowfly populations.

An age-structured deterministic model with multiple infections that accounts for decaying maternal antibody, waning infection-acquired and vaccine-induced immunity is formulated to study the transmission dynamics of pertussis and the effect of childhood DTaP and adolescent Tdap vaccines. The expression of the reproduction number ${ℛ}$ is derived for the ODE model in the case of proportionate mixing. Estimated age-dependent transmission probability and empirical contact data are used in the simulation of the ODE model from which the basic reproduction number ${{ℛ}}_0$ is estimated to be around 15. The combination of DTaP and Tdap vaccines fails to bring ${{ℛ}}_0$ under one and thus pertussis remains endemic despite sustained high coverage of vaccination. While both DTaP and Tdap vaccines have remarkable effect on reducing the incidences of the age groups being directly vaccinated, the adolescent booster dose Tdap is also found to provide some indirect protection for infants though very limited ($<5\%$ incidence reduction).

In this paper, we investigate the behavior of a predator–prey model with cooperation and Allee effect considering both deterministic and stochastic approaches. The main aim of this paper is to investigate the effect of environmental fluctuation in a deterministic predator–prey model. During the analysis of the deterministic model, it is shown that the system has saddle-node point of co-dimension 1, Hopf bifurcation and Bogdanov–Takens bifurcation of co-dimension 2. To study the effect of environmental fluctuation, we use perturbation to the birth rate of prey and death rate of predator density by Gaussian white noise. The persistence of the model and the stationary distribution is shown by forming a suitable Lyapunov function. Finally, numerical simulations are performed to validate the theoretical findings.

In this paper, an optimal control theory was applied to the tuberculosis (TB) model governed by system of nonlinear ordinary differential equations. The aim is to investigate the impact of treatment failure on the TB epidemic. An optimal control strategy is proposed to minimize the disease effect and cost incurred due to treatment failure. The existence and uniqueness of optimal controls are proved. The characterization of optimal paths is analytically derived using Pontryagin’s Minimum Principle. The control-induced model is then fitted using TB infected cases reported from the year 2010–2019 in East Shewa zone Oromia regional state, Ethiopia. Different simulation cases were performed to compare with analytical results. The simulation results show that the combined effect of awareness via various mass media and continuous supervision during the treatment period helps to reduce treatment failure and hence reduced the TB epidemic in the community.

In this study, we propose a deterministic model describing the dynamics of anthrax transmission in animals. It is assumed in the model that anthrax is contracted when susceptible animal comes into contact with infected animals, infected carcasses or the spores of Bacillus anthracis. Conditions for disease-free and endemic equilibria are derived and the basic reproduction number ($R_0$) is computed. The disease-free equilibrium is stable when $R_0<1$ and the disease will be eliminated. If $R_0>1$, the disease persists, therefore, the endemic equilibrium is globally stable. Further, we extend our model by applying optimal control problem in which vaccination for susceptible animals and sanitation are control variables to minimize the anthrax transmission. We study three strategies to investigate the impact of the controls. Our numerical results demonstrate that both vaccination and sanitation help minimizing the transmission although vaccination alone gives more significant impact than sanitation alone. However, the combination of both controls gives the best result in wiping out the anthrax transmission overall. Further, cost-effectiveness analysis shows that the most effective strategy to control anthrax disease is a combination of vaccination and sanitation of the infected areas, therefore these two interventions should be encouraged.

Predator–prey interactions are the ubiquitous and natural phenomenon in an ecological system. Predators reduce the prey population’s density by direct killing, which is an essential part of any ecological system. Based on the experimental works, for overcoming predation pressure, prey uses a variety of mechanisms. With Holling type-II functional response, we examined a prey–predator system incorporating anti-predator behavior and the cost of fear into prey. Prey anti-predator activity is a counterattacking strategy in which adult prey targets adolescent predators in order to counteract the potential predation pressure. Fear of predation may disrupt the physiological state of prey species and lead to long loss of prey species. In this study, we investigated this aspect to use a dynamical modeling approach. This research finds a plethora of fascinating phenomena. The studied system exhibits a wide range of dynamics and bifurcations, including saddle-node, Hopf, homoclinic, and a Bogdanov–Takens bifurcation in co-dimension two are among the dynamics and bifurcations observed in the analyzed system. We performed some numerical simulations to investigate the effects of anti-predator behavior and fear on prey and found both affect the prey–predator dynamics significantly. Our numerical examples clearly show that as prey carrying capacity increases, so does the prey’s ability to perceive the risk of predation.

There is a global decline in marine fish abundance due to unsustainable harvesting. An effective harvesting policy can protect the overfished population from possible extinction. In this study, we used a mathematical model characterized by density-dependent refuge protection for herbivorous fish, exhibiting an anti-predator response in presence of a generalist invasive fish. The anti-predator behavior entails predator density-dependent reduced fecundity of the herbivorous fish. The model assumes a continuous threshold harvesting policy (CTHP) for the herbivorous fish and uses the catch-per-unit-effort (CPUE) hypothesis for harvesting the invasive fish. The CTHP allows harvesting of the herbivorous fish only when the density of the herbivorous fish exceeds a specified threshold value, thus ensuring the long-term sustainability of the herbivorous fish stock. The existence and stability of steady-state solutions and the bifurcations of the model are investigated. Our study reveals that the level of apprehension of the herbivorous fish and fishing efforts will play a significant role in the stability of the system. We examine the existence of the bionomic equilibrium and then study the dynamic optimization of the harvesting policy by employing Pontryagin’s maximum principle. We discuss different subsidies and tax policies for the effective management of a sustainable fishery. We use numerical simulations to compare the revenues corresponding to the harvest policies based on maximum sustainable yield (MSY), maximum economic yield (MEY), and optimal sustainable yield (OSY) for inferring an ecologically sustainable and economically viable harvesting policy.

In this study, we investigate the effects of excessive inputs of bioavailable phosphorus into a lake from agricultural fields and households on algal bloom formation, and its potential management by using the lanthanum-modified clay Phoslock as a bioavailable phosphorus adsorbent. We also investigate the impact of time delay involved in the process of applying Phoslock after measuring the density of algal biomass in the lake. Moreover, the seasonal effects in the input of bioavailable phosphorus from the agricultural lands and the application rate of Phoslock have been investigated. Our simulation results show that the algal growth accelerates if the bioavailable phosphorus is excessively loaded through agricultural runoff and domestic discharges. However, algal biomass can be effectively controlled by employing Phoslock in a sufficiently large quantity. Further, we find that a delay in the application of Phoslock induces limit cycle oscillations. Furthermore, our findings show that the combined actions of delay and periodicity in the application of Phoslock bring forth dynamical complexity in the lake system by giving rise to higher periodic solutions and bursting patterns. Lastly, we investigate an optimal control problem to estimate the optimum dosage of Phoslock for the mitigation of algal biomass from the lake system.