Mainul Haque

• PhD
• Professor (Assistant) at University of Nottingham

Prey refuge from predators can play an important role in stabilising an ecological system by reducing interactions between species, while Allee effects can arise from a range of biological phenomena, such as anti-predator vigilance, genetic trends and feeding deficiencies. We develop a predator–prey model that combines these phenomena, considering...

Background: Primary blast lung injury (PBLI) presents as a syndrome of respiratory distress and haemoptysis resulting from explosive shock wave exposure and is a frequent cause of mortality and morbidity in both military conflicts and terrorist attacks. The optimal mode of mechanical ventilation for managing PBLI is not currently known, and clinic...

Primary blast lung injury is the most important component of a multisystem syndrome of injury that results from exposure to an explosive shockwave. The majority of such casualties require ventilation in an intensive care unit. We describe the use of a novel primary blast lung injury simulator to evaluate the potential efficacy of continuous positiv...

In this paper, a ratio-dependent food chain model has been considered. The total population has been divided into three classes, namely prey, predator and top-predator population. We have also incorporated intra-specific competition of predators in the model. We have studied the boundedness, dissipativeness and permanence of the solutions of the sy...

Bomb or explosion-blast injuries are likely to be increasingly encountered as terrorist activity increases and pre-hospital medical care improves. We therefore reviewed the epidemiology, pathophysiology and treatment of primary blast lung injury. In addition to contemporary military publications and expert recommendation, an EMBASE and MEDLINE sear...

Background Clinical trials have, so far, failed to establish clear beneficial outcomes of recruitment maneuvers (RMs) on patient mortality in acute respiratory distress syndrome (ARDS), and the effects of RMs on the cardiovascular system remain poorly understood. MethodsA computational model with highly integrated pulmonary and cardiovascular syste...

Primary blast lung injury frequently complicates military conflict and terrorist attacks on civilian populations. The fact that it occurs in areas of conflict or unpredictable mass casualty events makes clinical study in human casualties implausible. Research in this field is therefore reliant on the use of some form of biological or non-biological...

Background: Positive end-expiratory pressure (PEEP) is widely used to improve oxygenation and prevent alveolar collapse in mechanically ventilated patients with the acute respiratory distress syndrome (ARDS). While PEEP predictably improves arterial oxygenation, high PEEP strategies have demonstrated equivocal improvements in ARDS mortality. The ef...

Background Positive end-expiratory pressure (PEEP) is widely used to improve oxygenation and prevent alveolar collapse in mechanically ventilated patients with the acute respiratory distress syndrome (ARDS). Although PEEP improves arterial oxygenation predictably, high-PEEP strategies have demonstrated equivocal improvements in ARDS-related mortali...

This paper presents the methodology used in patient-specific calibration of a novel highly integrated model of the cardiovascular and pulmonary pathophysiology associated with Acute Respiratory Distress Syndrome (ARDS). We focus on data from previously published clinical trials on the static and dynamic cardio-pulmonary responses of three ARDS pati...

The present investigation deals with the analysis of the spatial pattern formation of a diffusive predator-prey system with ratio-dependent functional response involving the influence of intra-species competition among predators within two-dimensional space. The appropriate condition of Turing instability around the interior equilibrium point of th...

During mechanical ventilation, positive end-expiratory pressure (PEEP) is applied to the lungs of patients with acute respiratory distress syndrome (ARDS) to prevent collapse of open but unstable alveoli, and to recruit collapsed alveoli 1. PEEP has the potential to impair cardiac output. Despite finding a consistent improvement in oxygenation and...

Clinicians use oxygenation indices to diagnose and treat pulmonary diseases. These indices are acceptably helpful but not representing the lung status if there is a change in the external pulmonary factors such as (fraction of inspired oxygen(FIO2), haemoglobin(Hb), partial pressure of CO2(PaCO2) and oxygen consumption(VO2)). The aim of our study i...

We describe the development of an integrated cardiovascular and pulmonary model for use in the investigation of novel mechanical ventilation strategies in the intensive care unit. The cardiac model includes the cardiac chambers, the pulmonary circulation and the systemic circulation. The modeling of complex mechanisms for vascular segments, time va...

Direct comparison of the relative efficacy of different recruitment maneuvers (RMs) for patients with acute respiratory distress syndrome (ARDS) via clinical trials is difficult, due to the heterogeneity of patient populations and disease states, as well as a variety of practical issues. There is also significant uncertainty regarding the minimum v...

We propose two mathematical models for predator–prey interactions allowing for prey refuge. The novelty lies in the assumption that the amount of prey in refugia is proportional not only to the encounters between prey and predator, but also it is modelled by a Holling type II response function. The second model also accounts for predator's intraspe...

Computer simulation models could play a key role in developing novel therapeutic strategies for patients with chronic obstructive pulmonary disease (COPD) if they can be shown to accurately represent the pathophysiological characteristics of individual patients. We evaluated the capability of a computational simulator to reproduce the heterogeneous...

In this article, a predator–prey model of Beddington–DeAngelis type with discrete delay is proposed and analyzed. The essential mathematical features of the proposed model are investigated in terms of local, global analysis and bifurcation theory. By analyzing the associated characteristic equation, it is found that the Hopf bifurcation occurs when...

The current paper accounts for the influence of intra-specific competition among predators in a prey dependent tri-trophic food chain model of interacting populations. We offer a detailed mathematical analysis of the proposed food chain model to illustrate some of the significant results that has arisen from the interplay of deterministic ecologica...

The current paper deals with the mathematical models of predator-prey system where a transmissible disease spreads among the predator species only. Four mathematical models are proposed and analysed with several popular predator functional responses in order to show the influence of functional response on eco-epidemic models. The existence, bounded...

In the current paper, we propose a two-prey-one-predator system with Holling type II predation functional response where prey species consumes the remains of the other prey species' carcass given by their predator. Mathematical analysis of the proposed model equations with regard to non-negative invariance including stability and bifurcation are ca...

In this paper, spatial patterns of a Holling–Tanner predator-prey model subject to cross diffusion, which means the prey species exercise a self-defense mechanism to protect themselves from the attack of the predator are investigated. By using the bifurcation theory, the conditions of Hopf and Turing bifurcation critical line in a spatial domain ar...

A system of delay differential equation is proposed to account the effect of delay in the predator– prey model of interacting population. In this article, the modified ratio-dependent Bazykin model with delay in predator equation has been considered. The essential mathematical features of the proposed model are analyzed with the help of equilibria,...

The study of reaction-diffusion system constitutes some of the most fascinating developments of late twentieth century mathematics and biology. This article investigates complexity and chaos in the complex patterns dynamics of the original Beddington-DeAngelis predator-prey model which concerns the influence of intra species competition among preda...

Studies on stability mechanism and bifurcation analysis of a system of interacting populations by the combined effect of self as well as cross-diffusion become an important issue in ecology. In the current investigation we derive the conditions for existence and stability properties of a predator–prey interaction with the inclusion of self and cros...

Mathematical modelling of gene regulatory networks is a relatively new area which is playing an important role in theoretical and experimental investigations that seek to open the door to understanding the real mechanisms that take place in living systems. The current thesis concentrates on studying the animal stress-response gene regulatory networ...

Caenorhabditis elegans strains carrying stress-reporter green fluorescent protein transgenes were used to explore patterns of response to metals. Multiple stress pathways were induced at high doses by most metals tested, including members of the heat shock, oxidative stress, metallothionein (mtl) and xenobiotic response gene families. A mathematica...

The present investigation accounts for the influence of intra-specific competition among predators in the original Beddington-DeAngelis predator-prey model. We offer a detailed mathematical analysis of the model to describe some of the significant results that may be expected to arise from the interplay of deterministic and stochastic biological ph...

We consider a system of delay differential equations modeling the predator-prey ecoepidemic dynamics with a transmissible disease in the predator population. The time lag in the delay terms represents the predator gestation period. We analyze essential mathematical features of the proposed model such as local and global stability and in addition st...

The modified Leslie-Gower and Holling-type II predator-prey model is generalized in the context of ecoepidemiology, with disease spreading only among the prey species. A new feature is introduced, the intraspecific competition of infected prey. All the equilibria are characterized and the existence of a Hopf bifurcation at the coexistence equilibri...

Studies on stability mechanism and bifurcation analysis of a system of interacting populations by the combined effect of self and cross-diffusion become an important issue in ecology. In the current investigation, we derive the conditions for existence and stability properties of a predator-prey model under the influence of self and cross-diffusion...

A Leslie-Gower-Holling type II model is modified to introduce a contagious disease in the predator population, assuming that disease cannot propagate to the prey. All the system's equilibria are determined and the behaviour of the system near them is investigated. The main mathematical issues are global stability and bifurcations for some of the eq...

In this paper we propose a predator-prey model with logistic growth in the prey population that includes an SIS parasitic infection in the predator population, with the assumption that the predator has an alternative source of food. For simplicity we initially work with a model involving the fractions of the predator which are susceptible and those...

Stress-responsive genes belonging to multiple defensive pathways in the nematode C. elegans are cross-regulated by kinase signalling (AKT-1/-2, p38 MAPK) and transcription factors (DAF-16, SKN-1). This cross-talk between stress pathways implies that they are best regarded as a stress-response network (SRN), whose behaviour as a whole should be amen...

In this paper, we consider the dynamic behavior of an impulsive delay differential equation model with the effects of interspecific allelopathic interaction. A good understanding of the permanence, extinction and the existence of positive periodic solutions is gained. It turns out that the impulsive controls play a crucial role in shaping the above...

A system of impulsive differential equations describing predator–prey dynamics with impulsive effect is proposed and analyzed with the assumption that a transmissible disease is spreading among the prey species only. At first, the “semi-trivial” periodic solution (S(t),0,0) is given. After that, the existence of “infection-free” periodic solution (...

In this paper we study a predator-prey model with logistic growth in the prey population, where a disease spreads among the prey according to an susceptible-infected-susceptible (SIS) epidemic model. The predators do not consume infected prey. After a review of the literature we formulate the basic mathematical model. For simplicity, we work initia...

A modified Leslie–Gower-type prey–predator model with periodic impulsive perturbations is proposed and investigated. It is proved that there exists an asymptotically stable prey-free periodic solution when the impulsive period is less than some critical value. Otherwise, the above system can be permanent. And then the numerical simulations are carr...

This investigation accounts for epidemics spreading among interacting populations. The infective disease spreads among the prey, of which only susceptibles reproduce, while infected prey do not grow, recover, reproduce nor compete for resources. The model is general enough to describe a large number of ecosystems, on land, in the air or in the wate...

Ratio-dependent predator-prey models are increasingly favored by both the theoretical and experimental ecologists as a more suitable alternative to describe predator-prey interactions when the predators hunt seriously. In this article, the classical Bazykin's model is modified with ratio-dependent functional response. Stability and bifurcation situ...

Increasing evidence indicates that numerous genetic pathways responding to environmental stress in animals are regulated co-ordinately as well as independently. These stress-response systems should therefore be viewed in holistic terms as a network. As such, their behaviour is susceptible to mathematical modelling using a systems biology approach....

Symbiotic communities are relevant from the biologists' viewpoint. Diseases affecting interacting populations have earlier been considered in ecoepidemic models with interactions of competitive or predational type but also for mutualistic associations. Here the analysis is extended to populations experiencing mutualism, in the more realistic case i...

The Leslie–Gower predator–prey model with logistic growth in prey is here modified to include an SI parasitic infection affecting the prey population only. Thresholds are identified for the predator population to survive, and the conditions for the disease to die out naturally are given. The behavior of the system around each equilibrium is investi...

Holling-Tanner model is revised with ratio-dependent functional response since ratio-dependent functional response is more appropriate when predator involves serious searching process. The essential mathematical features of the modified model have been analyzed with the help of local stability, global stability, bifurcation theory. Finally, analyti...

We propose a ratio-dependent demographic predator-prey model in which also a disease spreads among predators via homogeneous mixing. Equilibria of the system are analysed, numerical evidence shows limit cycles to arise. The disease effects on the model are discussed. Comparisons of these findings with results of some related investigations allow th...

In this paper, a pulse vaccination and pulse destroying (or isolation) SIS model is proposed for integrated logistic type population dynamics and periodic infection rate beta(t). The dynamical behavior of the model is analyzed. The basic reproductive number R₀ is defined. It is proved that the infection-free periodic solution is globally...

A predator–prey model with transmissible disease in the prey species is proposed and analysed. The essential mathematical features are analysed with the help of equilibrium, local and global stability analyses and bifurcation theory. We find four possible equilibria. One is where the populations are extinct. Another is where the disease and predato...

The role of disease in ecological systems is a very important issue from both mathematical and ecological points of view. This paper deals with the qualitative analysis of a prey-dependent predator – prey system in which a disease is spreading among the prey species only. We have analysed the behaviour of the system around each equilibrium and obta...

Transmissible diseases are known to induce remarkable major behavioral changes in predator-prey systems. However, little attention has been paid to model such situations. The latter would allow to predict useful applications in both dynamics and control. Here the Holling-Tanner model is revisited to account for the influence of a transmissible dise...

The Salton Sea, the largest lake of California, is now facing problems due to its massive fish and bird mortality. Haque and Chattopadhyay1 have proposed and analyzed an eco-epidemiological model on Salton Sea. The present article deals with the global stability analysis of the positive interior equilibrium of that eco-epidemiological model. We use...

A pulse vaccination SIR model with periodic infection rate $\beta (t)$ have been proposed and studied. The basic reproductive number $R_0$ is defined. The dynamical behaviors of the model are analyzed with the help of persistence, bifurcation and global stability. It has been shown that the infection-free periodic solution is globally stable provid...

In this article, we have proposed an epidemic model by using probability cellular automata theory. The essential mathematical features are analyzed with the help of stability theory. We have given an alternative modelling approach for the spatiotemporal system which is more realistic and satisfactory from the practical point of view. A discrete and...

We propose a predator-prey model with an epidemic spreading only among the former by contact between a healthy individual and an infected. An infected cannot recover, once contacted the disease. The prey are assumed to grow logistically, the predators are distinguished between disease carriers and healthy individuals. Both feed only on the prey spe...

We modify an eco-epidemiological model proposed by J. Chattopadhyay and N. Bairagi [Math. Comput. Model. Dyn. Syst. 8, 257–272 (2002; Zbl 1020.92030)] by taking into account nonlinear incidence rates instead of bilinear incidenc rates as considered by Chattopadhyay and Bairagi. We observe that limit cycle oscillations around the positive interior e...