Ordinary Differential Equations and Applied Dynamics Commons^™

Tracking Food Quality In Algae-Daphnia Ecosystems Through Stage Structured Models And Colimitation, Tomas Ascoli

Biology and Medicine Through Mathematics Conference

No abstract provided.

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

(R1954) Fractional Order On Modeling The Transmission Of Devastative Covid-19 Infection: Efficacy Of Vaccination, Ashutosh Rajput, Tanvi ., Rajiv Aggarwal, Arpana Sharma, Shiv Kumar Sahdev, Manoj Kumar, Jaimala .

Applications and Applied Mathematics: An International Journal (AAM)

The second wave of COVID-19 is an unprecedented condition in India and began in mid February 2021. Individuals who were already suffering from other comorbidities were found with lung infection, and hence, the number of disease induced deaths were rising faster during the second wave in relation to the first wave. This paper has proposed a mathematical model with fractional order derivatives by correlating the model based number of infectives with the real number of infectives in India. For the system of fractional differential equations, a disease-free state has been computed and proved to be locally asymptotically stable with certain …

(R2032) Modeling The Effect Of Sanitation Effort On The Spread Of Carrier-Dependent Infectious Diseases Due To Environmental Degradation, Ram Naresh, Sandhya Rani Verma, J. B. Shukla, Manju Agarwal

Applications and Applied Mathematics: An International Journal (AAM)

In this present study, an SIS model is proposed and analyzed to study the effect of sanitation effort in controlling the spread of carrier-dependent infectious disease in a human habitat due to environmental degradation. The dynamics of the model consist of six dependent variables, the susceptible population density, infective population density, carrier population density, cumulative density of environmental degradation and the density of sanitation effort applied on carrier population and degraded environment. In the modeling process, the carrier population density and sanitation effort are modeled logistically and the degradation of the environment is assumed to be directly proportional to the …

(R2020) Dynamical Study And Optimal Harvesting Of A Two-Species Amensalism Model Incorporating Nonlinear Harvesting, Manoj Kumar Singh, Poonam .

Applications and Applied Mathematics: An International Journal (AAM)

This study proposes a two-species amensalism model with a cover to protect the first species from the second species, with the assumption that the growth of the second species is governed by nonlinear harvesting. Analytical and numerical analyses have both been done on this suggested ecological model. Boundedness and positivity of the solutions of the model are examined. The existence of feasible equilibrium points and their local stability have been discussed. In addition, the parametric conditions under which the proposed system is globally stable have been determined. It has also been shown, using the Sotomayor theorem, that under certain parametric …

(R1522) Modelling The Influence Of Desertic Aerosols On The Transmission Dynamics Of Neisseria Meningitidis Serogroup A, Francis Signing, Berge Tsanou, Samuel Bowong

Applications and Applied Mathematics: An International Journal (AAM)

This paper assesses the role of desert aerosols and vaccine on the transmission dynamics of Neisseria Meningitis serogroup A (NmA). It is biologically well-documented that the inhalation of aerosol dust and its presence in the nasal cavity weakens the nasopharyngeal mucosa by damaging the mucosal barrier and inhibiting the mucosal immune defenses of susceptible and vaccinated individuals. We address the latter by proposing and analyzing a mathematical model for the dynamics of NmA that specifically accounts for the fast progression of susceptible and vaccinated individuals to the invasive stage of the disease. We compute the basic reproduction number and use …

(R1980) Effect Of Climate Change On Brain Tumor, Pardeep Kumar, Sarita Jha, Rajiv Aggarwal, Govind Kumar Jha

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we introduce a new dynamical model addressing the variation in climate condition due the presence of microorganisms. We also introduce a new dynamical model of cancer growth which includes three interactive cell populations with drug free environment, namely tumor cells, healthy host cells, and immune effector cells. In this, we considered the super growth of tumor cells. For the choice of certain parameters, both of the systems exhibit chaotic behavior. The aim of this work is to design the controller to control the chaos and to provide sufficient conditions which achieve synchronization of two non-identical systems, which …

Stochastic Models Of Zoonotic Avian Influenza With Multiple Hosts, Environmental Transmission, And Migration In The Natural Reservoir, Kaia Smith

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

(R1468) Global Analysis Of An Seirs Model For Covid-19 Capturing Saturated Incidence With Treatment Response, David A. Oluyori, Helen O. Adebayo, Ángel G.C. Pérez

Applications and Applied Mathematics: An International Journal (AAM)

In this work, a new SEIRS model with saturated incidence rate and piecewise linear treatment response is proposed to describe the dynamics of COVID-19. It is assumed that the treatment response is proportional to the number of infected people as long as the incidence cases are within the capacity of the healthcare system, after which the value becomes constant, when the number of confirmed cases exceeds the carrying capacity of the available medical facilities. Thus, the basic reproduction number of the model is obtained. It is proved that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number …

(R1523) Abundant Natural Resources, Ethnic Diversity And Inclusive Growth In Sub-Saharan Africa: A Mathematical Approach, Juliet I. Adenuga, Kazeem B. Ajide, Anthonia T. Odeleye, Abayomi A. Ayoade

Applications and Applied Mathematics: An International Journal (AAM)

The sub-Saharan African region is blessed with abundant natural resources and diverse ethnic groups, yet the region is dominated by the largest number of poor people worldwide due to inequitable distribution of national income. Existing statistics forecast decay in the quality of lives over the years compared to the continent of Asia that shares similar history with the region. In this paper, a-five dimensional first-order nonlinear ordinary differential equations was formulated to give insight into various factors that shaped dynamics of inclusive growth in sub-Saharan Africa. The validity test was performed based on ample mathematical theorems and the model was …

(R1412) Stability And Bifurcation Of A Cholera Epidemic Model With Saturated Recovery Rate, Huda Abdul-Satar, Raid K. Naji

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a Cholera epidemic model is proposed and studied analytically as well as numerically. It is assumed that the disease is transmitted by contact with Vibrio cholerae and infected person according to dose-response function. However, the saturated treatment function is used to describe the recovery process. Moreover, the vaccine against the disease is assumed to be utterly ineffective. The existence, uniqueness and boundedness of the solution of the proposed model are discussed. All possible equilibrium points and the basic reproduction number are determined. The local stability and persistence conditions are established. Lyapunov method and the second additive compound …

(R1488) Transformation Of Glucokinase Under Variable Rate Constants And Thermal Conditions: A Mathematical Model, Mukhtar Ahmad Khanday, Roohi Bhat

Applications and Applied Mathematics: An International Journal (AAM)

The glucokinase (GK) in cells plays a pivotal role in the regulation of carbohydrate metabolism and acts as a sensor of glucose. It helps us to control glucose levels during fast and food intake conditions through triggering shifts in metabolism or cell functions. Various forms of hypoglycaemia and hyperglycaemia occur due to the transformations of the gene of the Glucokinase. The mathematical modelling of enzyme dynamics is an emerging research area to serve its role in biological investigations. Thus, it is imperative to establish a mathematical model to understand the kinetics of native and denatured forms of enzyme-GK under thermal …

Global Stability Of Generalized Within-Host Chikungunya Virus Dynamics Models, Taofeek O. Alade, Afeez Abidemi, Cemil Tunç, Shafeek A. Ghaleb

Applications and Applied Mathematics: An International Journal (AAM)

This paper proposes two models of a general nonlinear within-host Chikungunya virus (CHIKV) dynamics. The production, incidence, proliferation and removal rates of all compartments are modeled by general nonlinear functions that satisfy a set of reasonable conditions. The second model takes into consideration two forms of infected host cells: (i) latently infected cells which do not produce the CHIKV, (ii) actively infected cells which generate the CHIKV particles. We show that all the solutions of the models are nonnegative and bounded. The global stability of the steady states of the models is proven by applying Lyapunov method and LaSalle’s invariance …

Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria

Applications and Applied Mathematics: An International Journal (AAM)

The article aims to study a modified Leslie-Gower predator-prey model with Allee effect II, affecting the functional response with the assumption that the extent to which the environment provides protection to both predator and prey is the same. The model has been studied analytically as well as numerically, including stability and bifurcation analysis. Compared with the predator-prey model without Allee effect, it is found that the weak Allee effect II can bring rich and complicated dynamics, such as the model undergoes to a series of bifurcations (Homoclinic, Hopf, Saddle-node and Bogdanov-Takens). The existence of Hopf bifurcation has been shown for …

Covid-19 Modeling With Caution In Relaxing Control Measures And Possibilities Of Several Peaks In Cameroon, S. Y. Tchoumi, Y. T. Kouakep, D. J. Fotsa Mbogne, J. C. Kamgang, V. C. Kamla, D. Bekolle

Applications and Applied Mathematics: An International Journal (AAM)

We construct a new model for the comprehension of the Covid-19 dynamics in Cameroon. We present the basic reproduction number and perform some numerical analysis on the possible outcomes of the epidemic. The major results are the possibilities to have several peaks before the end of the first outbreak for an uniform strategy, and the danger to have a severe peak after the adoption of a careless strategy of barrier anti-Covid-19 measures that follow a good containment period.

Lexicographic Sensitivity Functions For Nonsmooth Models In Mathematical Biology, Matthew D. Ackley

Electronic Theses and Dissertations

Systems of ordinary differential equations (ODEs) may be used to model a wide variety of real-world phenomena in biology and engineering. Classical sensitivity theory is well-established and concerns itself with quantifying the responsiveness of such models to changes in parameter values. By performing a sensitivity analysis, a variety of insights can be gained into a model (and hence, the real-world system that it represents); in particular, the information gained can uncover a system's most important aspects, for use in design, control or optimization of the system. However, while the results of such analysis are desirable, the approach that classical theory …

Estimation Of Transmission Dynamics Of Covid-19 In India: The Influential Saturated Incidence Rate, - Tanvi, Rajiv Aggarwal, Ashutosh Rajput

Applications and Applied Mathematics: An International Journal (AAM)

A non-linear SEIR mathematical model for coronavirus disease in India has been proposed, by incorporating the saturated incidence rate on the occurrence of new infections. In the model, the threshold quantity known as the reproduction number is evaluated which determines the stability of disease-free equilibrium and the endemic equilibrium points. The disease-free equilibrium point becomes globally asymptotically stable when the corresponding reproduction number is less than unity, whereas, if it is greater than unity then the endemic equilibrium point comes into existence, which is locally asymptotically stable under certain restrictions on the parameters value in the model. The impact of …

Dynamical Behavior Of An Eco-Epidemiological Model Incorporating Prey Refuge And Prey Harvesting, Dawit Melese, Ousman Muhye, Subrata K. Sahu

Applications and Applied Mathematics: An International Journal (AAM)

In this paper an eco-epidemiological model incorporating a prey refuge and prey harvesting with disease in the prey-population is considered. Predators are assumed to consume both the susceptible and infected prey at different rates. The positivity and boundedness of the solution of the system are discussed. The existence and stability of the biologically feasible equilibrium points are investigated. Numerical simulations are performed to support our analytical findings.

Optimal Allocation Of Two Resources In Annual Plants, David Mcmorris

Department of Mathematics: Dissertations, Theses, and Student Research

The fitness of an annual plant can be thought of as how much fruit is produced by the end of its growing season. Under the assumption that annual plants grow to maximize fitness, we can use techniques from optimal control theory to understand this process. We introduce two models for resource allocation in annual plants which extend classical work by Iwasa and Roughgarden to a case where both carbohydrates and mineral nutrients are allocated to shoots, roots, and fruits in annual plants. In each case, we use optimal control theory to determine the optimal resource allocation strategy for the plant …

Viral Dynamics Of Delayed Ctl-Inclusive Hiv-1 Infection Model With Both Virus-To-Cell And Cell-To-Cell Transmissions, M. L. Mann Manyombe, J. Mbang, L. Nkague Nkamba, D. F. Nkoa Onana

Applications and Applied Mathematics: An International Journal (AAM)

We consider a mathematical model that describes a viral infection of HIV-1 with both virus-tocell and cell-to-cell transmission, CTL response immune and four distributed delays, describing intracellular delays and immune response delay. One of the main features of the model is that it includes a constant production rate of CTLs export from thymus, and an immune response delay. We derive the basic reproduction number and show that if the basic reproduction number is less than one, then the infection free equilibrium is globally asymptotically stable; whereas, if the basic reproduction number is greater than one, then there exist a chronic …

The Impact Of Nonlinear Harvesting On A Ratio-Dependent Holling-Tanner Predator-Prey System And Optimum Harvesting, Manoj Kumar Singh, B. S. Bhadauria

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a Holling-Tanner predator-prey model with ratio-dependent functional response and non-linear prey harvesting is analyzed. The mathematical analysis of the model includes existence, uniqueness and boundedness of positive solutions. It also includes the permanence, local stability and bifurcation analysis of the model. The ratio-dependent model always has complex dynamics in the vicinity of the origin; the dynamical behaviors of the system in the vicinity of the origin have been studied by means of blow up transformation. The parametric conditions under which bionomic equilibrium point exist have been derived. Further, an optimal harvesting policy has been discussed by using …

Tympanal Asymmetry In A Parasitoid Fly: Small Asymmetries Produce Big Gains, Max Mikel-Stites, Anne E. Staples

Biology and Medicine Through Mathematics Conference

No abstract provided.

Understanding The Fundamental Molecular Mechanism Of Osteogenic Differentiation From Mesenchymal Stem Cells, Imelda Trejo, Hristo V. Kojouharov

Applications and Applied Mathematics: An International Journal (AAM)

A mathematical model is presented to study the regulatory effects of growth factors in osteoblastogenesis. The model incorporates the interactions among mesenchymal stem cells, osteoblasts, and growth factors. The resulting system of nonlinear ordinary differential equations is studied analytically and numerically. Mathematical conditions for successful osteogenic differentiation and optimal osteoblasts population are formulated, which can be used in practice to accelerate bone formation. Numerical simulations are also presented to support the theoretical results and to explore different medical interventions to enhance osteoblastogenesis.

Bifurcation Analysis For Prey-Predator Model With Holling Type Iii Functional Response Incorporating Prey Refuge, Lazaar Oussama, Mustapha Serhani

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we carried out the bifurcation analysis for a Lotka-Volterra prey-predator model with Holling type III functional response incorporating prey refuge protecting a constant proportion of the preys. We study the local bifurcation considering the refuge constant as a parameter. From the center manifold equation, we establish a transcritical bifurcation for the boundary equilibrium. In addition, we prove the occurrence of Hopf bifurcation for the homogeneous equilibrium. Moreover, we give the radius and period of the unique limit cycle for our system

Dynamics In A Respiratory Control Model With Two Delays, Saroj P. Pradhan, Ferenc Hartung, Janos Turi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we study ventilation patterns in a set of parameter dependent nonlinear delay equations with two transport delays modeling the human respiratory control system with peripheral and central control loops. We present a convergent numerical scheme suitable to perform simulations when all disturbances and system parameters are known, then we consider the numerical identifiability of various system parameters based on ventilation data. We are especially interested in the identification of the transport delays in the control loops because these parameters are not measurable directly, but they have a strong influence on system stability/instability.

On The Weighted Pseudo Almost Periodic Solutions Of Nicholson’S Blowflies Equation, Ramazan Yazgan, Cemil Tunç

Applications and Applied Mathematics: An International Journal (AAM)

This study is concerned with the existence, uniqueness and global exponential stability of weighted pseudo almost periodic solutions of a generalized Nicholson’s blowflies equation with mixed delays. Using some differential inequalities and a fixed point theorem, sufficient conditions were obtained for the existence, uniqueness of at the least a weighted pseudo almost periodic solutions and global exponential stability of this solution. The results of this study are new and complementary to the previous ones can be found in the literature. At the end of the study an example is given to show the accuracy of our results.

Integrating Mathematics And Biology In The Classroom: A Compendium Of Case Studies And Labs, Becky Sanft, Anne Walter

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria

Applications and Applied Mathematics: An International Journal (AAM)

The article aims to study a modified Leslie-Gower predator-prey model with Allee effect II, affecting the functional response with the assumption that the extent to which the environment provides protection to both predator and prey is the same. The model has been studied analytically as well as numerically, including stability and bifurcation analysis. Compared with the predator-prey model without Allee effect, it is found that the weak Allee effect II can bring rich and complicated dynamics, such as the model undergoes to a series of bifurcations (Homoclinic, Hopf, Saddle-node and Bogdanov-Takens). The existence of Hopf bifurcation has been shown for …

Stability Of Delayed Virus Infection Model With A General Incidence Rate And Adaptive Immune Response, Zhimin Chen, Xiuxiang Liu, Zhongzhong Xie

Applications and Applied Mathematics: An International Journal (AAM)

We present the dynamical behaviors of a virus infection model with general infection rate, immune responses and two intracellular delays which describe the interactions of the HIV virus, target cells, CTL cells and antibodies within host. Three factors are incorporated in this model: (1) the intrinsic growth rate of uninfected cells, (2) a nonlinear incidence rate function considering both virus-tocell infection and cell-to-cell transmission, and (3) a nonlinear productivity and removal function. By the method of Lyapunov functionals and LaSalle’s invariance principle, we show that the global dynamics of the model is determined by the reproductive numbers for viral infection …

Parameter Estimation And Optimal Control Of The Dynamics Of Transmission Of Tuberculosis With Application To Cameroon, A. Temgoua, Y. Malong, J. Mbang, S. Bowong

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with the problem of parameter estimation and optimal control of a tuberculosis (TB) model with seasonal fluctuations. We first present a uncontrolled TB model with seasonal fluctuations. We present the theoretical analysis of the uncontrolled TB model without seasonal fluctuations. After, we propose a numerical study to estimate the unknown parameters of the TB model with seasonal fluctuations according to demographic and epidemiological data from Cameroon. Simulation results are in good accordance with the seasonal variation of the new active reported cases of TB in Cameroon. Using this TB model with seasonality, the tuberculosis control is formulated …