Modelling the role of opportunistic diseases in coinfection

2018 ◽  
Vol 13 (3) ◽  
pp. 28
Author(s):  
Marcos Marvá ◽  
Rafael Bravo de la Parra ◽  
Ezio Venturino
Keyword(s):  
Epidemic Model ◽  
Recovery Rate ◽  
Reproduction Number ◽  
Backward Bifurcation ◽  
Treatment Rate ◽  
Opportunistic Disease ◽  
Sis Epidemic Model ◽  
Primary Disease ◽  
Sis Epidemic

In this paper, we formulate a model for evaluating the effects of an opportunistic disease affecting only those individuals already infected by a primary disease. The opportunistic disease act on a faster time scale and it is represented by an SIS epidemic model with frequency-dependent transmission. The primary disease is governed by an SIS epidemic model with density-dependent transmission, and we consider two different recovery cases. The first one assumes a constant recovery rate whereas the second one takes into account limited treatment resources by means of a saturating treatment rate. No demographics is included in these models.Our results indicate that misunderstanding the role of the opportunistic disease may lead to wrong estimates of the overall potential amount of infected individuals. In the case of constant recovery rate, an expression measuring this discrepancy is derived, as well as conditions on the opportunistic disease imposing a coinfection endemic state on a primary disease otherwise tending to disappear. The case of saturating treatment rate adds the phenomenon of backward bifurcation, which fosters the presence of endemic coinfection and greater levels of infected individuals. Nevertheless, there are specific situations where increasing the opportunistic disease basic reproduction number helps to eradicate both diseases.

A simple SIS epidemic model with a backward bifurcation

2000 ◽  
Vol 40 (6) ◽  
pp. 525-540 ◽  
Author(s):  
P. van den Driessche ◽  
James Watmough
Keyword(s):  
Epidemic Model ◽  
Backward Bifurcation ◽  
Sis Epidemic Model ◽  
Sis Epidemic

scholarly journals A Stochastic SIS Epidemic Model with Ornstein-Uhlenbeck Process and Brown Motion

2021 ◽  
Author(s):  
Xingzhi Chen ◽  
Baodan Tian ◽  
Xin Xu ◽  
Ruoxi Yang ◽  
Shouming Zhong
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Global Solutions ◽  
Uhlenbeck Process ◽  
Sis Epidemic Model ◽  
Ornstein Uhlenbeck Process ◽  
Brown Motion ◽  
Sis Epidemic ◽  
The Basic Reproduction Number

Abstract This paper studies a stochastic differential equation SIS epidemic model, disturbed randomly by the mean-reverting Ornstein-Uhlenbeck process and Brownian motion. We prove the existence and uniqueness of the positive global solutions of the model and obtain the controlling conditions for the extinction and persistence of the disease. The results show that when the basic reproduction number Rs0 < 1, the disease will extinct, on the contrary, when the basic reproduction number Rs0 > 1, the disease will persist. Furthermore, we can inhibit the outbreak of the disease by increasing the intensity of volatility or decreasing the speed of reversion ϑ, respectively. Finally, we give some numerical examples to verify these results.

scholarly journals Dynamics of Stochastically Perturbed SIS Epidemic Model with Vaccination

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yanan Zhao ◽  
Daqing Jiang
Keyword(s):  
Epidemic Model ◽  
Death Rate ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Dynamical Behavior ◽  
Standard Technique ◽  
Deterministic Models ◽  
Sis Epidemic Model ◽  
Disease Free ◽  
Sis Epidemic

We introduce stochasticity into an SIS epidemic model with vaccination. The stochasticity in the model is a standard technique in stochastic population modeling. In the deterministic models, the basic reproduction numberR0is a threshold which determines the persistence or extinction of the disease. When the perturbation and the disease-related death rate are small, we carry out a detailed analysis on the dynamical behavior of the stochastic model, also regarding of the value ofR0. IfR0≤1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model, whereas, ifR0>1, there is a stationary distribution, which means that the disease will prevail. The results are illustrated by computer simulations.

scholarly journals An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks

2021 ◽  
Vol 18 (5) ◽  
pp. 6790-6805
Author(s):  
Meici Sun ◽  
◽  
Qiming Liu
Keyword(s):  
Time Delay ◽  
Epidemic Model ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Scale Free ◽  
Sis Epidemic Model ◽  
The Mean ◽  
Sis Epidemic

<abstract><p>An SIS epidemic model with time delay and stochastic perturbation on scale-free networks is established in this paper. And we derive sufficient conditions guaranteeing extinction and persistence of epidemics, respectively, which are related to the basic reproduction number $ R_0 $ of the corresponding deterministic model. When $ R_0 &lt; 1 $, almost surely exponential extinction and $ p $-th moment exponential extinction of epidemics are proved by Razumikhin-Mao Theorem. Whereas, when $ R_0 &gt; 1 $, the system is persistent in the mean under sufficiently weak noise intensities, which indicates that the disease will prevail. Finally, the main results are demonstrated by numerical simulations.</p></abstract>

Equilibriums of an SIS Epidemic Model

2014 ◽  
Vol 678 ◽  
pp. 103-106
Author(s):  
Jing Hai Wang
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Death Rate ◽  
Birth Rate ◽  
Reproduction Number ◽  
Nonlinear Incidence Rate ◽  
Sis Epidemic Model ◽  
Disease Free ◽  
Sis Epidemic ◽  
The Basic Reproduction Number

An SIS epidemic model with nonlinear incidence rate is considered. At the same time we decide that the birth rate is equal to death rate. We get the basic reproduction number . We analyze the existences of the equilibriums of the system. There are some endemic equilibriums and one disease-free equilibrium of the system.

scholarly journals A Bistable Phenomena Induced by a Mean-Field SIS Epidemic Model on Complex Networks: A Geometric Approach

2021 ◽  
Vol 9 ◽  
Author(s):  
Xiaoyan Wang ◽  
Junyuan Yang
Keyword(s):  
Complex Networks ◽  
Epidemic Model ◽  
Mean Field ◽  
Geometric Approach ◽  
Backward Bifurcation ◽  
Medical Resources ◽  
Epidemic Curve ◽  
Sis Epidemic Model ◽  
Lag Effect ◽  
Sis Epidemic

In this paper, we propose a degree-based mean-field SIS epidemic model with a saturated function on complex networks. First, we adopt an edge-compartmental approach to lower the dimensions of such a proposed system. Then we give the existence of the feasible equilibria and completely study their stability by a geometric approach. We show that the proposed system exhibits a backward bifurcation, whose stabilities are determined by signs of the tangent slopes of the epidemic curve at the associated equilibria. Our results suggest that increasing the management and the allocation of medical resources effectively mitigate the lag effect of the treatment and then reduce the risk of an outbreak. Moreover, we show that decreasing the average of a network sufficiently eradicates the disease in a region or a country.

scholarly journals Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yakui Xue ◽  
Junfeng Wang
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Backward Bifurcation ◽  
Disease Spread ◽  
Treatment Rate ◽  
Stability Of Equilibria ◽  
Existence And Stability ◽  
The Basic Reproduction Number

An epidemic model with infectious force in infected and immune period and treatment rate of infectious individuals is proposed to understand the effect of the capacity for treatment of infective on the disease spread. It is assumed that treatment rate is proportional to the number of infective below the capacity and is constant when the number of infective is greater than the capacity. It is proved that the existence and stability of equilibria for the model is not only related to the basic reproduction number but also the capacity for treatment of infective. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low.

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