scholarly journals Mathematical Modeling of the Coinfection Dynamics of Malaria-Toxoplasmosis in the Tropics

2019 ◽  
Vol 56 (2) ◽  
pp. 139-163
Author(s):  
Oluwatayo M. Ogunmiloro
Keyword(s):  
Reproduction Number ◽  
Model System ◽  
Host Population ◽  
Globally Asymptotically Stable ◽  
Susceptible Host ◽  
Tropical Regions ◽  
First Order ◽  
Mathematical Techniques ◽  
The Tropics ◽  
The Impact

SummaryCoinfection by Plasmodium species and Toxoplasma gondii in humans is widespread, with its endemic impact mostly felt in the tropics. A mathematical model is formulated as a first-order nonlinear system of ordinary differential equations to describe the coinfection dynamics of malaria-toxoplasmosis in the mainly human and feline susceptible host population in tropical regions. Comprehensive mathematical techniques are applied to show that the model system is bounded, positive and realistic in an epidemiological sense. Also, the basic reproduction number (Romt) of the coinfection model is obtained. It is shown that if Romt < 1, the model system at its malaria-toxoplasmosis absent equilibrium is both locally and globally asymptotically stable. The impact of toxoplasmosis and its treatment on malaria, and vice versa, is studied and analyzed. Sensitivity analysis was performed to investigate the impact of the model system parameters on the reproduction number of the transmission of malaria-toxoplasmosis coinfection. Simulations and graphical illustrations were made to validate the results obtained from the theoretical model.

scholarly journals Local and global asymptotic behavior of malaria-filariasis coinfections in compliant and noncompliant susceptible pregnant women to antenatal medical program in the tropics

2019 ◽  
Vol 2019 (1) ◽  
pp. 31-54
Author(s):  
Oluwatayo M. Ogunmiloro
Keyword(s):  
Pregnant Women ◽  
Host Population ◽  
Control Measures ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Susceptible Host ◽  
Medical Program ◽  
Manifold Theory ◽  
The Tropics ◽  
Parameter Values

Abstract In this paper, a mathematical nonlinear model system of equations describing the dynamics of the co-interaction between malaria and filariasis epidemic affecting the susceptible host population of pregnant women in the tropics is formulated. The basic reproduction number Rmf of the coepidemic model is obtained, and we investigated that it is the threshold parameter between the extinction and persistence of the coepidemic disease. If Rmf < 1, then the disease-free steady state is both locally and globally asymptotically stable resulting in the disease dying out of the host. Also, if Rmf > 1, the disease lingers on. The center manifold theory is used to show that the unique endemic equilibrium is locally asymptotically stable. However, variations in the parameter values involved in the model build up will bring about appropriate control measures to curtail the spread of the coepidemic disease. Numerical simulations are carried out to confirm the theoretical results.

NUMERICAL AND STABILITY ANALYSIS OF THE TRANSMISSION DYNAMICS OF SVIR EPIDEMIC MODEL WITH STANDARD INCIDENCE RATE

2019 ◽  
Vol 4 (2) ◽  
pp. 349 ◽  
Author(s):  
Oluwatayo Michael Ogunmiloro ◽  
Fatima Ohunene Abedo ◽  
Hammed Kareem
Keyword(s):  
Reproduction Number ◽  
Disease Spread ◽  
Asymptotically Stable ◽  
Equilibrium Solutions ◽  
Transform Method ◽  
Globally Asymptotically Stable ◽  
Differential Transform ◽  
Mathematical Techniques ◽  
Fourth Order Method ◽  
Theoretical Results

In this article, a Susceptible – Vaccinated – Infected – Recovered (SVIR) model is formulated and analysed using comprehensive mathematical techniques. The vaccination class is primarily considered as means of controlling the disease spread. The basic reproduction number (Ro) of the model is obtained, where it was shown that if Ro<1, at the model equilibrium solutions when infection is present and absent, the infection- free equilibrium is both locally and globally asymptotically stable. Also, if Ro>1, the endemic equilibrium solution is locally asymptotically stable. Furthermore, the analytical solution of the model was carried out using the Differential Transform Method (DTM) and Runge - Kutta fourth-order method. Numerical simulations were carried out to validate the theoretical results. 

scholarly journals Threshold Dynamics in a Model for Zika Virus Disease with Seasonality

2021 ◽  
Vol 83 (4) ◽  
Author(s):  
Mahmoud A. Ibrahim ◽  
Attila Dénes
Keyword(s):  
Zika Virus ◽  
Reproduction Number ◽  
Virus Disease ◽  
Threshold Dynamics ◽  
Global Dynamics ◽  
Threshold Parameter ◽  
Globally Asymptotically Stable ◽  
Linear Integral ◽  
The Impact ◽  
Disease Free

AbstractWe present a compartmental population model for the spread of Zika virus disease including sexual and vectorial transmission as well as asymptomatic carriers. We apply a non-autonomous model with time-dependent mosquito birth, death and biting rates to integrate the impact of the periodicity of weather on the spread of Zika. We define the basic reproduction number $${\mathscr {R}}_{0}$$ R 0 as the spectral radius of a linear integral operator and show that the global dynamics is determined by this threshold parameter: If $${\mathscr {R}}_0 < 1,$$ R 0 < 1 , then the disease-free periodic solution is globally asymptotically stable, while if $${\mathscr {R}}_0 > 1,$$ R 0 > 1 , then the disease persists. We show numerical examples to study what kind of parameter changes might lead to a periodic recurrence of Zika.

scholarly journals Evaluating the role of contracting and expanding rainforest in initiating cycles of speciation across the Isthmus of Panama

2012 ◽  
Vol 279 (1742) ◽  
pp. 3520-3526 ◽  
Author(s):  
Brian Tilston Smith ◽  
Amei Amei ◽  
John Klicka
Keyword(s):  
Bird Species ◽  
Tropical Regions ◽  
Isthmus Of Panama ◽  
Species Pairs ◽  
The Matrix ◽  
High Species Richness ◽  
The Rich ◽  
The Tropics ◽  
The Impact

Climatic and geological changes across time are presumed to have shaped the rich biodiversity of tropical regions. However, the impact climatic drying and subsequent tropical rainforest contraction had on speciation has been controversial because of inconsistent palaeoecological and genetic data. Despite the strong interest in examining the role of climatic change on speciation in the Neotropics there has been few comparative studies, particularly, those that include non-rainforest taxa. We used bird species that inhabit humid or dry habitats that dispersed across the Panamanian Isthmus to characterize temporal and spatial patterns of speciation across this barrier. Here, we show that these two assemblages of birds exhibit temporally different speciation time patterns that supports multiple cycles of speciation. Evidence for these cycles is further corroborated by the finding that both assemblages consist of ‘young’ and ‘old’ species, despite dry habitat species pairs being geographically more distant than pairs of humid habitat species. The matrix of humid and dry habitats in the tropics not only allows for the maintenance of high species richness, but additionally this study suggests that these environments may have promoted speciation. We conclude that differentially expanding and contracting distributions of dry and humid habitats was probably an important contributor to speciation in the tropics.

scholarly journals Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jianping Wang ◽  
Shujing Gao ◽  
Yueli Luo ◽  
Dehui Xie
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Logistic Growth ◽  
Threshold Dynamics ◽  
Global Dynamics ◽  
Globally Asymptotically Stable ◽  
Linear Integral ◽  
The Impact ◽  
Disease Free ◽  
The Basic Reproduction Number

We analyze the impact of seasonal activity of psyllid on the dynamics of Huanglongbing (HLB) infection. A new model about HLB transmission with Logistic growth in psyllid insect vectors and periodic coefficients has been investigated. It is shown that the global dynamics are determined by the basic reproduction numberR0which is defined through the spectral radius of a linear integral operator. IfR0< 1, then the disease-free periodic solution is globally asymptotically stable and ifR0> 1, then the disease persists. Numerical values of parameters of the model are evaluated taken from the literatures. Furthermore, numerical simulations support our analytical conclusions and the sensitive analysis on the basic reproduction number to the changes of average and amplitude values of the recruitment function of citrus are shown. Finally, some useful comments on controlling the transmission of HLB are given.

scholarly journals A Mathematical Model for Nipah Virus Infection

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Assefa Denekew Zewdie ◽  
Sunita Gakkhar
Keyword(s):  
Virus Infection ◽  
Reproduction Number ◽  
Initial Conditions ◽  
Nipah Virus ◽  
Virus Transmission ◽  
Globally Asymptotically Stable ◽  
Dead Bodies ◽  
Manifold Theory ◽  
The Impact ◽  
The Given

It has been reported that unprotected contact with the dead bodies of infected individuals is a plausible way of Nipah virus transmission. An SIRD model is proposed in this paper to investigate the impact of unprotected contact with dead bodies of infected individuals before burial or cremation and their disposal rate on the dynamics of Nipah virus infection. The model is analyzed, and the reproduction number is computed. It is established that the disease-free state is globally asymptotically stable when the reproduction number is less than unity and unstable if it is greater than unity. By using the central manifold theory, we observe that the endemic equilibrium is locally stable near to unity. It is concluded that minimizing unsafe contact with the infected dead body and/or burial or cremation as fast as possible contributes positively. Further, the numerical simulations for the given choice of data and initial conditions illustrate that the endemic state is stable and the disease persists in the community when the reproduction number is greater than one.

scholarly journals Synthesizing within-host and population-level selective pressures on viral populations: the impact of adaptive immunity on viral immune escape

2010 ◽  
Vol 7 (50) ◽  
pp. 1311-1318 ◽  
Author(s):  
Igor Volkov ◽  
Kim M. Pepin ◽  
James O. Lloyd-Smith ◽  
Jayanth R. Banavar ◽  
Bryan T. Grenfell
Keyword(s):  
Evolutionary Dynamics ◽  
Immune Escape ◽  
Adaptive Immune Response ◽  
Population Level ◽  
Analytical Framework ◽  
Host Population ◽  
Host Immunity ◽  
Host Cells ◽  
Susceptible Host ◽  
The Impact

The evolution of viruses to escape prevailing host immunity involves selection at multiple integrative scales, from within-host viral and immune kinetics to the host population level. In order to understand how viral immune escape occurs, we develop an analytical framework that links the dynamical nature of immunity and viral variation across these scales. Our epidemiological model incorporates within-host viral evolutionary dynamics for a virus that causes acute infections (e.g. influenza and norovirus) with changes in host immunity in response to genetic changes in the virus population. We use a deterministic description of the within-host replication dynamics of the virus, the pool of susceptible host cells and the host adaptive immune response. We find that viral immune escape is most effective at intermediate values of immune strength. At very low levels of immunity, selection is too weak to drive immune escape in recovered hosts, while very high levels of immunity impose such strong selection that viral subpopulations go extinct before acquiring enough genetic diversity to escape host immunity. This result echoes the predictions of simpler models, but our formulation allows us to dissect the combination of within-host and transmission-level processes that drive immune escape.

scholarly journals Seasonality Impact on the Transmission Dynamics of Tuberculosis

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Yali Yang ◽  
Chenping Guo ◽  
Luju Liu ◽  
Tianhua Zhang ◽  
Weiping Liu
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Autonomous Systems ◽  
Positive Periodic Solution ◽  
Transmission Dynamics ◽  
Uniform Persistence ◽  
Globally Asymptotically Stable ◽  
The Impact ◽  
Disease Free ◽  
The Basic Reproduction Number

The statistical data of monthly pulmonary tuberculosis (TB) incidence cases from January 2004 to December 2012 show the seasonality fluctuations in Shaanxi of China. A seasonality TB epidemic model with periodic varying contact rate, reactivation rate, and disease-induced death rate is proposed to explore the impact of seasonality on the transmission dynamics of TB. Simulations show that the basic reproduction number of time-averaged autonomous systems may underestimate or overestimate infection risks in some cases, which may be up to the value of period. The basic reproduction number of the seasonality model is appropriately given, which determines the extinction and uniform persistence of TB disease. If it is less than one, then the disease-free equilibrium is globally asymptotically stable; if it is greater than one, the system at least has a positive periodic solution and the disease will persist. Moreover, numerical simulations demonstrate these theorem results.

The impact of media coverage with a piecewise transmission rate in the spread of diseases

2016 ◽  
Vol 10 (01) ◽  
pp. 1750003
Author(s):  
Maoxing Liu ◽  
Lixia Zuo
Keyword(s):  
Basic Reproduction Number ◽  
Media Coverage ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Three Dimensional ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Contact Transmission ◽  
The Impact ◽  
The Basic Reproduction Number

A three-dimensional compartmental model with media coverage is proposed to describe the real characteristics of its impact in the spread of infectious diseases in a given region. A piecewise continuous transmission rate is introduced to describe that media coverage exhibits its effect only when the number of the infected exceeds a certain critical level. Further, it is assumed that the impact of media coverage on the contact transmission is described by an exponential decreasing factor. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity. On the other hand, when the basic reproduction number is greater than unity and media coverage impact is sufficiently small, a unique endemic equilibrium exists, which is globally asymptotically stable.

scholarly journals Optimal intervention strategies of staged progression HIV infections through an age-structured model with probabilities of ART drop out

2021 ◽  
Author(s):  
Ramsès Djidjou-Demasse
Keyword(s):  
Global Analysis ◽  
Hiv Infections ◽  
Host Population ◽  
Drop Out ◽  
Globally Asymptotically Stable ◽  
Optimal Intervention ◽  
Age Structured ◽  
Age Structured Model ◽  
The Impact ◽  
Disease Free

In this paper, we construct a model to describe the transmission of HIV in a homogeneous host population. By considering the specific mechanism of HIV, we derive a model structured in three successive stages: (i) primary infection, (ii) long phase of latency without symptoms and (iii) AIDS. Each HIV stage is stratified by the duration for which individuals have been in the stage, leading to a continuous age-structure model. In the first part of the paper, we provide a global analysis of the model depending upon the basic reproduction number R0. When R0<=1, then the disease-free equilibrium is globally asymptotically stable and the infection is cleared in the host population. On the contrary, if R0>1, we prove the epidemic's persistence with the asymptotic stability of the endemic equilibrium. By performing the sensitivity analysis, we then determine the impact of control-related parameters of the outbreak severity. For the second part, the initial model is extended with intervention methods. By taking into account ART interventions and the probability of treatment drop out, we discuss optimal interventions methods which minimize the number of AIDS cases.

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