scholarly journals A malaria transmission model with seasonal mosquito life-history traits

2018 ◽  
Author(s):  
Ramsès Djidjou-Demasse ◽  
Gbenga J. Abiodun ◽  
Abiodun M. Adeola ◽  
Joel O. Botai
Keyword(s):  
Life History ◽  
Stationary State ◽  
Disease Transmission ◽  
Human Disease ◽  
Life History Traits ◽  
Global Analysis ◽  
Positive Periodic Solution ◽  
Host Population ◽  
Transmission Model ◽  
Disease Free

AbstractIn this paper we develop and analyse a malaria model with seasonality of mosquito life-history traits: periodic-mosquitoes per capita birth rate, -mosquitoes death rate, -probability of mosquito to human disease transmission, -probability of human to mosquito disease transmission and -mosquitoes biting rate. All these parameters are assumed to be time dependent leading to a nonautonomous differential equation systems. We provide a global analysis of the model depending on two thresholds parametersand(with). When, then the disease-free stationary state is locally asymptotically stable. In the presence of the human disease-induced mortality, the global stability of the disease-free stationary state is guarantied when. On the contrary, if, the disease persists in the host population in the long term and the model admits at least one positive periodic solution. Moreover, by a numerical simulation, we show that a subcritical (backward) bifurcation is possible at. Finally, the simulation results are in accordance with the seasonal variation of the reported cases of a malaria-epidemic region in Mpumalanga province in South Africa.

scholarly journals Dynamics Analysis of an Avian Influenza A (H7N9) Epidemic Model with Vaccination and Seasonality

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Juping Zhang ◽  
Yun Li ◽  
Zhen Jin ◽  
Huaiping Zhu
Keyword(s):  
Avian Influenza ◽  
Influenza A ◽  
Reproduction Number ◽  
Positive Periodic Solution ◽  
Human Infection ◽  
Transmission Model ◽  
H7n9 Infection ◽  
Simulation Results ◽  
Theoretical Results ◽  
Disease Free

H7N9 virus in the environment plays a role in the dynamics of avian influenza A (H7N9). A nationwide poultry vaccination with H7N9 vaccine program was implemented in China in October of 2017. To analyze the effect of vaccination and environmental virus on the development of avian influenza A (H7N9), we establish an avian influenza A (H7N9) transmission model with vaccination and seasonality among human, birds, and poultry. The basic reproduction number for the prevalence of avian influenza is obtained. The global stability of the disease-free equilibrium and the existence of positive periodic solution are proved by the comparison theorem and the asymptotic autonomous system theorem. Finally, we use numerical simulations to demonstrate the theoretical results. Simulation results indicate that the risk of H7N9 infection is higher in colder environment. Vaccinating poultry can significantly reduce human infection.

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.

scholarly journals A Dengue Vaccination Model for Immigrants in a Two-Age-Class Population

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Hengki Tasman ◽  
Asep K. Supriatna ◽  
Nuning Nuraini ◽  
Edy Soewono
Keyword(s):  
Disease Transmission ◽  
Disease Status ◽  
Host Population ◽  
Reproduction Ratio ◽  
Vaccination Programs ◽  
Vector Population ◽  
Dengue Transmission ◽  
Existence And Stability ◽  
Adult Classes ◽  
Disease Free

We develop a model of dengue transmission with some vaccination programs for immigrants. We classify the host population into child and adult classes, in regards to age structure, and into susceptible, infected and recovered compartments, in regards to disease status. Since migration plays important role in disease transmission, we include immigration and emigration factors into the model which are distributed in each compartment. Meanwhile, the vector population is divided into susceptible, exposed, and infectious compartments. In the case when there is no incoming infected immigrant, we obtain the basic reproduction ratio as a threshold parameter for existence and stability of disease-free and endemic equilibria. Meanwhile, in the case when there are some incoming infected immigrants, we obtain only endemic equilibrium. This indicates that screening for the immigrants is important to ensure the effectiveness of the disease control.

scholarly journals A model of malaria population dynamics with migrants

2021 ◽  
Vol 18 (6) ◽  
pp. 7301-7317
Author(s):  
Peter Witbooi ◽  
◽  
Gbenga Abiodun ◽  
Mozart Nsuami
Keyword(s):  
South African ◽  
Disease Transmission ◽  
Indoor Residual Spraying ◽  
Host Population ◽  
Equilibrium Existence ◽  
Vector Population ◽  
Using Data ◽  
Special Case ◽  
Disease Free

<abstract><p>We present a compartmental model in ordinary differential equations of malaria disease transmission, accommodating the effect of indoor residual spraying on the vector population. The model allows for influx of infected migrants into the host population and for outflow of recovered migrants. The system is shown to have positive solutions. In the special case of no infected immigrants, we prove global stability of the disease-free equilibrium. Existence of a unique endemic equilibrium point is also established for the case of positive influx of infected migrants. As a case study we consider the combined South African malaria region. Using data covering 31 years, we quantify the effect of malaria infected immigrants on the South African malaria region.</p></abstract>

scholarly journals Unravelling Transmission in Epidemiological Models and its Role in the Disease-Diversity Relationship

2021 ◽  
Author(s):  
Marjolein E.M. Toorians ◽  
Ailene MacPherson ◽  
T. Jonathan Davies
Keyword(s):  
Disease Transmission ◽  
Disease Outbreaks ◽  
Host Population ◽  
Pathogen Transmission ◽  
Transmission Model ◽  
General Function ◽  
Transmission Method ◽  
Model Framework ◽  
Host Diversity ◽  
Transmission Mechanisms

With the decrease of biodiversity worldwide coinciding with an increase in disease outbreaks, investigating this link is more important then ever before. This review outlines the different modelling methods commonly used for pathogen transmission in animal host systems. There are a multitude of ways a pathogen can invade and spread through a host population. The assumptions of the transmission model used to capture disease propagation determines the outbreak potential, the net reproductive success (R0). This review offers an insight into the assumptions and motivation behind common transmission mechanisms and introduces a general framework with which contact rates, the most important parameter in disease dynamics, determines the transmission method. By using a general function introduced here and this general transmission model framework, we provide a guide for future disease ecologists for how to pick the contact function that best suites their system. Additionally, this manuscript attempts to bridge the gap between mathematical disease modelling and the controversially and heavily debated disease-diversity relationship, by expanding the summarized models to multiple hosts systems and explaining the role of host diversity in disease transmission. By outlining the mechanisms of transmission into a stepwise process, this review will serve as a guide to model pathogens in multi-host systems. We will further describe these models it in the greater context of host diversity and its effect on disease outbreaks, by introducing a novel method to include host species&rsquo; evolutionary history into the framework.

scholarly journals The Combined Effects of Bacterial Symbionts and Aging on Life History Traits in the Pea Aphid, Acyrthosiphon pisum

2013 ◽  
Vol 80 (2) ◽  
pp. 470-477 ◽  
Author(s):  
Alice M. Laughton ◽  
Maretta H. Fan ◽  
Nicole M. Gerardo
Keyword(s):  
Life History ◽  
Life History Traits ◽  
Acyrthosiphon Pisum ◽  
Immune Cell ◽  
Host Population ◽  
Pea Aphid ◽  
Combined Effects ◽  
Content Type ◽  
Secondary Symbiont ◽  
Cell Counts

ABSTRACTWhile many endosymbionts have beneficial effects on hosts under specific ecological conditions, there can also be associated costs. In order to maximize their own fitness, hosts must facilitate symbiont persistence while preventing symbiont exploitation of resources, which may require tight regulation of symbiont populations. As a host ages, the ability to invest in such mechanisms may lessen or be traded off with demands of other life history traits, such as survival and reproduction. Using the pea aphid,Acyrthosiphon pisum, we measured survival, lifetime fecundity, and immune cell counts (hemocytes, a measure of immune capacity) in the presence of facultative secondary symbionts. Additionally, we quantified the densities of the obligate primary bacterial symbiont,Buchnera aphidicola, and secondary symbionts across the host's lifetime. We found life history costs to harboring some secondary symbiont species. Secondary symbiont populations were found to increase with host age, whileBuchnerapopulations exhibited a more complicated pattern. Immune cell counts peaked at the midreproductive stage before declining in the oldest aphids. The combined effects of immunosenescence and symbiont population growth may have important consequences for symbiont transmission and maintenance within a host population.

scholarly journals Effects of Coinfection on the Dynamics of Two Pathogens in a Tick-Host Infection Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Bei Sun ◽  
Xue Zhang ◽  
Marco Tosato
Keyword(s):  
Disease Transmission ◽  
Host Population ◽  
Infection Model ◽  
Uniform Persistence ◽  
Reproduction Numbers ◽  
Boundary Equilibrium ◽  
Tick Borne Disease ◽  
Host Infection ◽  
The Impact ◽  
Disease Free

As both ticks and hosts may carry one or more pathogens, the phenomenon of coinfection of multiple tick-borne diseases becomes highly relevant and plays a key role in tick-borne disease transmission. In this paper, we propose a coinfection model involving two tick-borne diseases in a tick-host population and calculate the basic reproduction numbers at the disease-free equilibrium and two boundary equilibria. To explore the impact of coinfection, we also derive the invasion reproduction numbers which indicate the potential of a pathogen to persist when another pathogen already exists in tick and host populations. Then, we obtain the global stability of the system at the disease-free equilibrium and the boundary equilibrium, respectively, and further demonstrate the existence conditions for uniform persistence of the two diseases. The final numerical simulations mainly verify the theoretical results of coinfection.

On the approximate solutions and asymptotic stability of an onchocerciasis transmission model

2021 ◽  
pp. 2150043
Author(s):  
Oluwatayo Michael Ogunmiloro
Keyword(s):  
Disease Transmission ◽  
Approximate Solutions ◽  
Host Population ◽  
Transmission Model ◽  
Asymptotically Stable ◽  
River Blindness ◽  
State Equations ◽  
Transform Method ◽  
Globally Asymptotically Stable ◽  
Incomplete Resistance

This article describes the mathematical model derivation describing river blindness disease transmission in human and vector (blackflies) host population. The effect of incomplete resistance to re-infection in human individuals who recovered from the disease after treatment but are still subjected to repeated exposures to infected blackflies bite is investigated. Also, the basic reproduction number [Formula: see text] is obtained and it is shown that if [Formula: see text], the onchocerciasis-free equilibrium is locally and globally asymptotically stable. Also, if [Formula: see text], the onchocerciasis-endemic equilibrium is globally asymptotically stable. Moreover, the Differential Transform Method (DTM) and Runge–Kutta fourth-order method is employed via the computational software Maple 18 to solve and obtain the approximate solutions of the model system equations, which showed that the numerical results favorably compare with each other. Simulations reveal that increase in biting and transmission rates leads to an increase of [Formula: see text] and incomplete resistance to re-infection due to consistent exposure to blackflies bites. Also, simulations of the approximate solutions of the model state equations are provided.

Effect of two commercial herbicides on life history traits of a human disease vector, Aedes aegypti, in the laboratory setting

Ecotoxicology ◽  
2016 ◽  
Vol 25 (5) ◽  
pp. 863-870 ◽  
Author(s):  
Alexandra Morris ◽  
Ebony G. Murrell ◽  
Talan Klein ◽  
Bruce H. Noden
Keyword(s):  
Life History ◽  
Aedes Aegypti ◽  
Human Disease ◽  
Life History Traits ◽  
Laboratory Setting ◽  
Disease Vector
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