scholarly journals Modeling Cell-to-Cell Spread of HIV-1 with Nonlocal Infections

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaoting Fan ◽  
Yi Song ◽  
Wencai Zhao
Keyword(s):  
Reproduction Number ◽  
Reaction Diffusion ◽  
Threshold Dynamics ◽  
Delayed Reaction ◽  
Heterogeneous Model ◽  
Host Environment ◽  
Reaction Diffusion Model ◽  
Globally Attractive ◽  
Cell Spread ◽  
Hiv 1

This paper is devoted to develop a nonlocal and time-delayed reaction-diffusion model for HIV infection within host cell-to-cell viral transmissions. In a bounded spatial domain, we study threshold dynamics in terms of basic reproduction number R0 for the heterogeneous model. Our results show that if R0<1, the infection-free steady state is globally attractive, implying infection becomes extinct, while if R0>1, virus will persist in the host environment.

scholarly journals Dynamic analysis of a malaria reaction-diffusion model with periodic delays and vector bias

2022 ◽  
Vol 19 (3) ◽  
pp. 2538-2574
Author(s):  
Hongyong Zhao ◽  
◽  
Yangyang Shi ◽  
Xuebing Zhang ◽  
◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Diffusion Model ◽  
Disease Transmission ◽  
Reaction Diffusion ◽  
Major Effect ◽  
Threshold Dynamics ◽  
Seasonal Temperature ◽  
Reaction Diffusion Model ◽  
Maturity Period ◽  
Globally Attractive

<abstract><p>One of the most important vector-borne disease in humans is malaria, caused by <italic>Plasmodium</italic> parasite. Seasonal temperature elements have a major effect on the life development of mosquitoes and the development of parasites. In this paper, we establish and analyze a reaction-diffusion model, which includes seasonality, vector-bias, temperature-dependent extrinsic incubation period (EIP) and maturation delay in mosquitoes. In order to get the model threshold dynamics, a threshold parameter, the basic reproduction number $ R_{0} $ is introduced, which is the spectral radius of the next generation operator. Quantitative analysis indicates that when $ R_{0} &lt; 1 $, there is a globally attractive disease-free $ \omega $-periodic solution; disease is uniformly persistent in humans and mosquitoes if $ R_{0} &gt; 1 $. Numerical simulations verify the results of the theoretical analysis and discuss the effects of diffusion and seasonality. We study the relationship between the parameters in the model and $ R_{0} $. More importantly, how to allocate medical resources to reduce the spread of disease is explored through numerical simulations. Last but not least, we discover that when studying malaria transmission, ignoring vector-bias or assuming that the maturity period is not affected by temperature, the risk of disease transmission will be underestimate.</p></abstract>

scholarly journals Impact of Regional Difference in Recovery Rate on the Total Population of Infected for a Diffusive SIS Model

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 888
Author(s):  
Jumpei Inoue ◽  
Kousuke Kuto
Keyword(s):  
Recovery Rate ◽  
Regional Difference ◽  
Total Population ◽  
Reproduction Number ◽  
Reaction Diffusion ◽  
Logistic Equation ◽  
Sis Model ◽  
Reaction Diffusion Model ◽  
Diffusive Logistic Equation ◽  
Sis Epidemic

This paper is concerned with an SIS epidemic reaction-diffusion model. The purpose of this paper is to derive some effects of the spatial heterogeneity of the recovery rate on the total population of infected and the reproduction number. The proof is based on an application of our previous result on the unboundedness of the ratio of the species to the resource for a diffusive logistic equation. Our pure mathematical result can be epidemically interpreted as that a regional difference in the recovery rate can make the infected population grow in the case when the reproduction number is slightly larger than one.

scholarly journals Analysis of a diffusive cholera model incorporating latency and bacterial hyperinfectivity

2021 ◽  
Vol 20 (11) ◽  
pp. 3921
Author(s):  
Wei Yang ◽  
Jinliang Wang
Keyword(s):  
Lyapunov Functional ◽  
Global Attractivity ◽  
Reproduction Number ◽  
Reaction Diffusion ◽  
Threshold Dynamics ◽  
Positive Equilibrium ◽  
Flux Boundary Condition ◽  
Nonlocal Reaction ◽  
Theoretical Results ◽  
The Basic Reproduction Number

<p style='text-indent:20px;'>In this paper, we are concerned with the threshold dynamics of a diffusive cholera model incorporating latency and bacterial hyperinfectivity. Our model takes the form of spatially nonlocal reaction-diffusion system associated with zero-flux boundary condition and time delay. By studying the associated eigenvalue problem, we establish the threshold dynamics that determines whether or not cholera will spread. We also confirm that the threshold dynamics can be determined by the basic reproduction number. By constructing Lyapunov functional, we address the global attractivity of the unique positive equilibrium whenever it exists. The theoretical results are still hold for the case when the constant parameters are replaced by strictly positive and spatial dependent functions.</p>

scholarly journals Analysis of a Diffusive Heroin Epidemic Model in a Heterogeneous Environment

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Jinliang Wang ◽  
Hongquan Sun
Keyword(s):  
Steady State ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Reaction Diffusion ◽  
Threshold Dynamics ◽  
Heterogeneous Environment ◽  
Threshold Parameter ◽  
Simulation Results ◽  
Heroin Model

This paper is concerned with a reaction-diffusion heroin model in a bound domain. The objective of this paper is to explore the threshold dynamics based on threshold parameter and basic reproduction number (BRN) ℜ0, and it is proved that if ℜ0<1, heroin spread will be extinct, while if ℜ0>1, heroin spread is uniformly persistent and there exists a positive heroin-spread steady state. We also obtain that the explicit formula of ℜ0 and global attractiveness of constant positive steady state (PSS) when all parameters are positive constants. Our simulation results reveal that compared to the homogeneous setting, the spatial heterogeneity has essential impacts on increasing the risk of heroin spread.

scholarly journals Existence of Traveling Wave Solutions for Cholera Model

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Tianran Zhang ◽  
Qingming Gou ◽  
Xiaoli Wang
Keyword(s):  
Traveling Wave ◽  
Wave Speed ◽  
Shooting Method ◽  
Reproduction Number ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Traveling Wave Solution ◽  
Reaction Diffusion Model ◽  
Minimal Wave Speed ◽  
The Basic Reproduction Number

To investigate the spreading speed of cholera, Codeço’s cholera model (2001) is developed by a reaction-diffusion model that incorporates both indirect environment-to-human and direct human-to-human transmissions and the pathogen diffusion. The two transmission incidences are supposed to be saturated with infective density and pathogen density. The basic reproduction numberR0is defined and the formula for minimal wave speedc*is given. It is proved by shooting method that there exists a traveling wave solution with speedcfor cholera model if and only ifc≥c*.

scholarly journals TRAVELING WAVE SOLUTIONS IN A STAGE-STRUCTURED DELAYED REACTION-DIFFUSION MODEL WITH ADVECTION

2015 ◽  
Vol 20 (2) ◽  
pp. 168-187
Author(s):  
Liang Zhang ◽  
Huiyan Zhao
Keyword(s):  
Diffusion Model ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Stage Structure ◽  
Delayed Reaction ◽  
Wave Solutions ◽  
Reaction Diffusion Model ◽  
Travelling Fronts ◽  
Appl Math

We investigate a stage-structured delayed reaction-diffusion model with advection that describes competition between two mature species in water flow. Time delays are incorporated to measure the time lengths from birth to maturity of the populations. We show there exists a finite positive number c∗ that can be characterized as the slowest spreading speed of traveling wave solutions connecting two mono-culture equilibria or connecting a mono-culture with the coexistence equilibrium. The model and mathematical result in [J.F.M. Al-Omari, S.A. Gourley, Stability and travelling fronts in Lotka–Volterra competition models with stage structure, SIAM J. Appl. Math. 63 (2003) 2063–2086] are generalized.

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