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

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.

Download Full-text

A model of malaria population dynamics with migrants

Mathematical Biosciences and Engineering ◽

10.3934/mbe.2021361 ◽

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>

Download Full-text

Global dynamics and bifurcation analysis of a fractional-order SEIR epidemic model with saturation incidence rate

10.22541/au.162530373.38917682/v1 ◽

2021 ◽

Author(s):

Parvaiz Ahmad Naik ◽

Muhammad Bilal Ghori ◽

Jian Zu ◽

Zohre Eskandari ◽

Mehraj-ud-din Naik

Keyword(s):

Incidence Rate ◽

Fractional Order ◽

Epidemic Model ◽

Disease Transmission ◽

Disease Status ◽

Host Population ◽

Sensitivity Analyses ◽

Feasible Region ◽

Global Dynamics ◽

Globally Stable

The present paper studies a fractional-order SEIR epidemic model for the transmission dynamics of infectious diseases such as HIV and HBV that spreads in the host population. The total host population is considered bounded, and Holling type-II saturation incidence rate is involved as the infection term. Using the proposed SEIR epidemic model, the threshold quantity, namely basic reproduction number R0, is obtained that determines the status of the disease, whether it dies out or persists in the whole population. The model’s analysis shows that two equilibria exist, namely, disease-free equilibrium (DFE) and endemic equilibrium (EE). The global stability of the equilibria is determined using a Lyapunov functional approach. The disease status can be verified based on obtained threshold quantity R0. If R0 < 1, then DFE is globally stable, leading to eradicating the population’s disease. If R0 > 1, a unique EE exists, and that is globally stable under certain conditions in the feasible region. The Caputo type fractional derivative is taken as the fractional operator. The bifurcation and sensitivity analyses are also performed for the proposed model that determines the relative importance of the parameters into disease transmission. The numerical solution of the model is obtained by the generalized Adams- Bashforth-Moulton method. Finally, numerical simulations are performed to illustrate and verify the analytical results.

Download Full-text

Susceptible host availability modulates climate effects on dengue dynamics

10.1101/2019.12.20.883363 ◽

2019 ◽

Author(s):

Nicole Nova ◽

Ethan R. Deyle ◽

Marta S. Shocket ◽

Andrew J. MacDonald ◽

Marissa L. Childs ◽

...

Keyword(s):

Disease Transmission ◽

Population Level ◽

Host Population ◽

Interactive Effects ◽

Climate Data ◽

Negative Effects ◽

Susceptible Host ◽

Susceptible Population ◽

Incidence Data ◽

Dengue Transmission

AbstractExperiments and models suggest that climate affects mosquito-borne disease transmission. However, disease transmission involves complex nonlinear interactions between climate and population dynamics, which makes detecting climate drivers at the population level challenging. By analyzing incidence data, estimated susceptible population size, and climate data with methods based on nonlinear time series analysis (collectively referred to as empirical dynamic modeling), we identified drivers and their interactive effects on dengue dynamics in San Juan, Puerto Rico. Climatic forcing arose only when susceptible availability was high: temperature and rainfall had net positive and negative effects, respectively. By capturing mechanistic, nonlinear, and context-dependent effects of population susceptibility, temperature, and rainfall on dengue transmission empirically, our model improves forecast skill over recent, state-of-the-art models for dengue incidence. Together, these results provide empirical evidence that the interdependence of host population susceptibility and climate drive dengue dynamics in a nonlinear and complex, yet predictable way.

Download Full-text

A malaria transmission model with seasonal mosquito life-history traits

10.1101/377184 ◽

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.

Download Full-text

ASSESSING THE EFFECTS OF TEMPERATURE AND DENGUE VIRUS LOAD ON DENGUE TRANSMISSION

Journal of Biological System ◽

10.1142/s0218339015500278 ◽

2015 ◽

Vol 23 (04) ◽

pp. 1550027 ◽

Cited By ~ 15

Author(s):

LOURDES ESTEVA ◽

HYUN MO YANG

Keyword(s):

Disease Transmission ◽

Basic Reproductive Number ◽

Effect Of Temperature ◽

Reproductive Number ◽

Vector Population ◽

Dengue Transmission ◽

Mosquito Mortality ◽

Different Temperatures ◽

Effects Of Temperature ◽

Nonzero Equilibrium

In this study, we propose a model to assess the effect of temperature on the incidence of dengue fever. For this, we take into account the dependence of the entomological and epidemiological parameters of the transmitter vector Aedes aegypti with respect to the temperature. The model consists of an ODE system that describes the transmission between humans and mosquitoes considering the aquatic stage of the vector population. The qualitative analysis of the model is made in terms of the parameters [Formula: see text] and [Formula: see text], which represent the basic offspring of mosquitoes, and the basic reproductive number of the disease, respectively. If [Formula: see text] mosquito population extinguishes while for [Formula: see text] it tends asymptotically to a nonzero equilibrium. Analogously, the disease transmission is eliminated if [Formula: see text], and it approaches an endemic equilibrium for [Formula: see text]. Using entomological data of mosquitoes as well as experimental data of disease transmission we evaluate [Formula: see text] and [Formula: see text] at different temperatures, obtaining that around [Formula: see text]C both parameters attain their maximum. Sensitivity analysis reveals that infection rates and mosquito mortality are the parameters for which [Formula: see text] is more sensitive.

Download Full-text

Bifurcation Analysis in Models for Vector-Borne Diseases with Logistic Growth

The Scientific World JOURNAL ◽

10.1155/2014/195864 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9

Author(s):

Guihua Li ◽

Zhen Jin

Keyword(s):

Death Rate ◽

Host Population ◽

Backward Bifurcation ◽

Logistic Growth ◽

Natural Death ◽

Vector Borne Diseases ◽

Vector Population ◽

Existence And Stability ◽

Vector Borne ◽

Parameter Varying

We establish and study vector-borne models with logistic and exponential growth of vector and host populations, respectively. We discuss and analyses the existence and stability of equilibria. The model has backward bifurcation and may have no, one, or two positive equilibria when the basic reproduction numberR0is less than one and one, two, or three endemic equilibria whenR0is greater than one under different conditions. Furthermore, we prove that the disease-free equilibrium is stable ifR0is less than 1, it is unstable otherwise. At last, by numerical simulation, we find rich dynamical behaviors in the model. By taking the natural death rate of host population as a bifurcation parameter, we find that the system may undergo a backward bifurcation, saddle-node bifurcation, Hopf bifurcation, Bogdanov-Takens bifurcation, and cusp bifurcation with the saturation parameter varying. The natural death rate of host population is a crucial parameter. If the natural death rate is higher, then the host population and the disease will die out. If it is smaller, then the host and vector population will coexist. If it is middle, the period solution will occur. Thus, with the parameter varying, the disease will spread, occur periodically, and finally become extinct.

Download Full-text

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

Complexity ◽

10.1155/2020/5615173 ◽

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.

Download Full-text

Mathematical Modeling of Yellow Fever Transmission Dynamics with Multiple Control Measures

Asian Research Journal of Mathematics ◽

10.9734/arjom/2019/v13i430112 ◽

2019 ◽

pp. 1-15 ◽

Cited By ~ 1

Author(s):

Tunde T. Yusuf ◽

David O. Daniel

Keyword(s):

Yellow Fever ◽

Disease Transmission ◽

Control Measures ◽

Transmission Dynamics ◽

Equilibrium Solutions ◽

Multiple Control ◽

Mosquito Net ◽

Vector Population ◽

The World ◽

Existence And Stability

Yellow-fever disease remains endemic in some parts of the world despite the availability of a potent vaccine and effective treatment for the disease. This necessitates continuous research to possibly eradicate the spread of the disease and its attendant burden. Consequently, a deterministicmodel for Yellow-fever disease transmission dynamics within the human and vector population is considered. The model equilibrium solutions are obtained while the criteria for their existence and stability are investigated. The model is solved numerically using the forth order Runge- Kunta scheme and the results are simulated for different scenarios of interest. Findings from the simulations show that the disease will continue to be prevalent in our society (no matter how small) as long as the immunity conferred by the available vaccine is not lifelong and the Yellowfever infected mosquitoes continue to have unhindered access to humans. Thus, justifying the wisdom behind the practice of continuous vaccination and the use of mosquito net in areas of high Yellow-fever endemicity. However, it was equally found that the magnitude of the Yellowfever outbreak can be remarkably reduced to a negligible level with the adoption of chemical or biological control measures which ensure that only mosquitoes with minimal biting tendency thrive in the environment.

Download Full-text

Analysis of A Coendemic Model of COVID-19 and Dengue Disease

Communication in Biomathematical Sciences ◽

10.5614/cbms.2021.4.2.5 ◽

2021 ◽

Vol 4 (2) ◽

pp. 138-151

Author(s):

Hilda Fahlena ◽

Widya Oktaviana ◽

Farida Farida ◽

Sudirman Sudirman ◽

Nuning Nuraini ◽

...

Keyword(s):

Limit Cycle ◽

Deterministic Model ◽

Transmission Rate ◽

Stable Limit Cycle ◽

Stable Limit ◽

Reproduction Ratio ◽

Dengue Disease ◽

Dengue Transmission ◽

Stable Periodic ◽

Disease Free

The coronavirus disease 2019 (COVID-19) pandemic continues to spread aggressively worldwide, infecting more than 170 million people with confirmed cases, including more than 3 million deaths. This pandemic is increasingly exacerbating the burden on tropical and subtropical regions of the world due to the pre-existing dengue fever, which has become endemic for a longer period in the same region. Co-circulation dengue and COVID-19 cases have been found and confirmed in several countries. In this paper, a deterministic model for the coendemic of COVID-19 and dengue is proposed. The basic reproduction ratio is obtained, which is related to the four equilibria, disease-free, endemic-COVID-19, endemic-dengue, and coendemic equilibria. Stability analysis is done for the first three equilibria. Furthermore, a condition for coexistence equilibrium is obtained, which gives a condition for bifurcation analysis. Numerical simulations were carried out to obtain a stable limit-cycle resulting from two Hopf bifurcation points with dengue transmission rate and COVID-19 transmission rate as the bifurcation parameter, representing a stable periodic coexistence of dengue and COVID-19 transmission. We identify the period of limit cycle decreases after reaching the maximum value.

Download Full-text

Modeling the Impact of Screening on the Transmission Dynamics of Human Papillomavirus with Optimal Control

WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL ◽

10.37394/23203.2021.16.66 ◽

2021 ◽

Vol 16 ◽

pp. 735-754

Author(s):

Eshetu Dadi Gurmu ◽

Boka Kumsa Bola ◽

Purnachandra Rao Koya

Keyword(s):

Optimal Control ◽

Human Papillomavirus ◽

Disease Transmission ◽

Control Strategies ◽

Equilibrium Points ◽

Screening Strategy ◽

Existence And Stability ◽

The Stability ◽

The Impact ◽

Disease Free

In this study, a nonlinear deterministic mathematical model of Human Papillomavirus was formulated. The model is studied qualitatively using the stability theory of differential equations. The model is analyzed qualitatively for validating the existence and stability of disease ¬free and endemic equilibrium points using a basic reproduction number that governs the disease transmission. It's observed that the model exhibits a backward bifurcation and the sensitivity analysis is performed. The optimal control problem is designed by applying Pontryagin maximum principle with three control strategies viz. prevention strategy, treatment strategy, and screening strategy. Numerical results of the optimal control model reveal that a combination of prevention, screening, and treatment is the most effective strategy to wipe out the disease in the community.

Download Full-text