scholarly journals STATIONARY DISTRIBUTION AND EXTINCTION OF STOCHASTIC CORONAVIRUS (COVID-19) EPIDEMIC MODEL

Fractals ◽  
2021 ◽  
Author(s):  
AMIR KHAN ◽  
HEDAYAT ULLAH ◽  
MOSTAFA ZAHRI ◽  
USA WANNASINGHA HUMPHRIES ◽  
TOURIA KARITE ◽  
...  
Keyword(s):  
Brownian Motion ◽  
Lyapunov Function ◽  
Unique Solution ◽  
Epidemic Model ◽  
Feasible Region ◽  
Random Perturbations ◽  
Suggested Model ◽  
Susceptible Population ◽  
Ergodic Distribution ◽  
Very High

The aim of this paper is to model corona-virus (COVID-19) taking into account random perturbations. The suggested model is composed of four different classes i.e. the susceptible population, the smart lockdown class, the infectious population, and the recovered population. We investigate the proposed problem for the derivation of at least one unique solution in the positive feasible region of nonlocal solution. For one stationary ergodic distribution, the necessary result of existence is developed by applying the Lyapunov function and the condition for the extinction of the disease is also established. The obtained results show that the effect of Brownian motion and noise terms on the transmission of the epidemic is very high. If the noise is large the infection may decrease or vanish. For validation of our obtained scheme, the results for all the classes of the problem have been simulated numerically.

Random perturbations of recursive sequences with an application to an epidemic model

1995 ◽  
Vol 32 (3) ◽  
pp. 559-578 ◽  
Author(s):  
Daniel Pierre Loti Viaud
Keyword(s):  
Dynamical System ◽  
Lyapunov Function ◽  
Finite Number ◽  
Epidemic Model ◽  
Sample Path ◽  
Random Perturbations ◽  
Main Condition ◽  
Limit Sets ◽  
Discrete Time Dynamical System ◽  
Recursive Sequences

We investigate the asymptotic sample path behaviour of a randomly perturbed discrete-time dynamical system. We consider the case where the trajectories of the non-perturbed dynamical system are attracted by a finite number of limit sets and characterize a case where this property remains valid for the perturbed dynamical system when the perturbation converges to zero. For this purpose, no further assumptions on the perturbation are needed and our main condition applies to the limit sets of the non-perturbed dynamical system. When the limit sets reduce to limit points we show that this main condition is more general than the usual assumption of the existence of a Lyapunov function for the non-perturbed dynamical system. An application to an epidemic model is given to illustrate our results.

Random perturbations of recursive sequences with an application to an epidemic model

1995 ◽  
Vol 32 (03) ◽  
pp. 559-578 ◽  
Author(s):  
Daniel Pierre Loti Viaud
Keyword(s):  
Dynamical System ◽  
Lyapunov Function ◽  
Finite Number ◽  
Epidemic Model ◽  
Sample Path ◽  
Random Perturbations ◽  
Main Condition ◽  
Limit Sets ◽  
Discrete Time Dynamical System ◽  
Recursive Sequences

We investigate the asymptotic sample path behaviour of a randomly perturbed discrete-time dynamical system. We consider the case where the trajectories of the non-perturbed dynamical system are attracted by a finite number of limit sets and characterize a case where this property remains valid for the perturbed dynamical system when the perturbation converges to zero. For this purpose, no further assumptions on the perturbation are needed and our main condition applies to the limit sets of the non-perturbed dynamical system. When the limit sets reduce to limit points we show that this main condition is more general than the usual assumption of the existence of a Lyapunov function for the non-perturbed dynamical system. An application to an epidemic model is given to illustrate our results.

scholarly journals Stabilization of Stochastic Differential Equations Driven by G-Brownian Motion with Aperiodically Intermittent Control

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 988
Author(s):  
Pengju Duan
Keyword(s):  
Brownian Motion ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Differential Equations ◽  
Mild Solution ◽  
Intermittent Control

The paper is devoted to studying the exponential stability of a mild solution of stochastic differential equations driven by G-Brownian motion with an aperiodically intermittent control. The aperiodically intermittent control is added into the drift coefficients, when intermittent intervals and coefficients satisfy suitable conditions; by use of the G-Lyapunov function, the p-th exponential stability is obtained. Finally, an example is given to illustrate the availability of the obtained results.

scholarly journals Extinction and persistence of a stochastic SIRV epidemic model with nonlinear incidence rate

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ramziya Rifhat ◽  
Zhidong Teng ◽  
Chunxia Wang
Keyword(s):  
Epidemic Model ◽  
Control Strategies ◽  
Random Perturbations ◽  
Disease Dynamics ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Analysis Theory ◽  
Lyapunov Function Method ◽  
Random Fluctuations ◽  
Theoretical Results

AbstractIn this paper, a stochastic SIRV epidemic model with general nonlinear incidence and vaccination is investigated. The value of our study lies in two aspects. Mathematically, with the help of Lyapunov function method and stochastic analysis theory, we obtain a stochastic threshold of the model that completely determines the extinction and persistence of the epidemic. Epidemiologically, we find that random fluctuations can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics. In other words, neglecting random perturbations overestimates the ability of the disease to spread. The numerical simulations are given to illustrate the main theoretical results.

scholarly journals Evaluation of Resistance Development in Bemisia tabaci Genn. (Homoptera: Aleyrodidae) in Cotton against Different Insecticides

Insects ◽  
2021 ◽  
Vol 12 (11) ◽  
pp. 996
Author(s):  
Muhammad Zaryab Khalid ◽  
Sohail Ahmed ◽  
Ibrahim Al-ashkar ◽  
Ayman EL Sabagh ◽  
Liyun Liu ◽  
...  
Keyword(s):  
Bemisia Tabaci ◽  
The Other ◽  
Resistance Development ◽  
Susceptible Population ◽  
Low Level ◽  
Development Of Resistance ◽  
Major Pest ◽  
Selection For ◽  
High Level ◽  
Very High

Cotton is a major crop of Pakistan, and Bemisia tabaci (Homoptera: Aleyrodidae) is a major pest of cotton. Due to the unwise and indiscriminate use of insecticides, resistance develops more readily in the whitefly. The present study was conducted to evaluate the resistance development in the whitefly against the different insecticides that are still in use. For this purpose, the whitefly population was selected with five concentrations of each insecticide, for five generations. At G1, compared with the laboratory susceptible population, a very low level of resistance was observed against bifenthrin, cypermethrin, acetamiprid, imidacloprid, thiamethoxam, nitenpyram, chlorfenapyr, and buprofezin with a resistance ratio of 3-fold, 2-fold, 1-fold, 4-fold, 3-fold, 3-fold, 3-fold, and 3-fold, respectively. However, the selection for five generations increased the resistance to a very high level against buprofezin (127-fold), and to a high level against imidacloprid (86-fold) compared with the laboratory susceptible population. While, a moderate level of resistance was observed against cypermethrin (34-fold), thiamethoxam (34-fold), nitenpyram (30-fold), chlorfenapyr (29-fold), and acetamiprid (21-fold). On the other hand, the resistance was low against bifenthrin (18-fold) after selection for five generations. A very low level of resistance against the field population of B. tabaci, at G1, showed that these insecticides are still effective, and thus can be used under the field conditions for the management of B. tabaci. However, the proper rotation of insecticides among different groups can help to reduce the development of resistance against insecticides.

Resistance to Aryloxyphenoxypropionate and Cyclohexanedione Herbicides in Wild Oat (Avena fatua)

Weed Science ◽  
1993 ◽  
Vol 41 (2) ◽  
pp. 232-238 ◽  
Author(s):  
Ian M. Heap ◽  
Bruce G. Murray ◽  
Heather A. Loeppky ◽  
Ian N. Morrison
Keyword(s):  
Dry Matter ◽  
Cross Resistance ◽  
Western Canada ◽  
Wild Oat ◽  
Recommended Dosage ◽  
Susceptible Population ◽  
South Central ◽  
Repeated Applications ◽  
High Level ◽  
Very High

Resistance to aryloxyphenoxypropionate and cyclohexanedione herbicides was identified in four wild oat populations from western Canada. Populations UM1, UM2, and UM3 originated from northwestern Manitoba and UM33 from south-central Saskatchewan. Field histories indicated that these populations were exposed to repeated applications of diclofop-methyl and sethoxydim over the previous 10 yr. The populations differed in their levels and patterns of cross-resistance to these and five other acetyl-CoA carboxylase inhibitors (ACCase inhibitors). UM1, UM2, and UM3 were resistant to diclofop-methyl, fenoxaprop-p-ethyl, and sethoxydim. In contrast, UM33 was resistant to the aryloxyphenoxy propionate herbicides but not to sethoxydim. The dose of sethoxydim required to reduce growth of UM1 by 50% was 150 times greater than for a susceptible population (UM5) or UM33 based on shoot dry matter reductions 21 d after treatment. This population differed from UM2 and UM3 that had R/S ratios of less than 10. In the field UM1 also exhibited a very high level of resistance to sethoxydim. In contrast to susceptible plants that were killed at the recommended dosage, shoot dry matter of resistant plants treated at eight times the recommended dosage was reduced by only 27%. In growth chamber experiments none of the four populations was cross-resistant to herbicides from five different chemical families.

scholarly journals Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 328 ◽  
Author(s):  
Yanli Ma ◽  
Jia-Bao Liu ◽  
Haixia Li
Keyword(s):  
Lyapunov Function ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, an SIQR (Susceptible, Infected, Quarantined, Recovered) epidemic model with vaccination, elimination, and quarantine hybrid strategies is proposed, and the dynamics of this model are analyzed by both theoretical and numerical means. Firstly, the basic reproduction number R 0 , which determines whether the disease is extinct or not, is derived. Secondly, by LaSalles invariance principle, it is proved that the disease-free equilibrium is globally asymptotically stable when R 0 < 1 , and the disease dies out. By Routh-Hurwitz criterion theory, we also prove that the disease-free equilibrium is unstable and the unique endemic equilibrium is locally asymptotically stable when R 0 > 1 . Thirdly, by constructing a suitable Lyapunov function, we obtain that the unique endemic equilibrium is globally asymptotically stable and the disease persists at this endemic equilibrium if it initially exists when R 0 > 1 . Finally, some numerical simulations are presented to illustrate the analysis results.

Deterministic and stochastic epidemics with several kinds of susceptibles

1985 ◽  
Vol 17 (01) ◽  
pp. 1-22 ◽  
Author(s):  
Frank Ball
Keyword(s):  
Epidemic Model ◽  
Susceptible Population ◽  
Basic Model ◽  
Spread Of Infection

We consider the spread of a general epidemic amongst a population consisting of invididuals with differing susceptibilities to the disease. Deterministic and stochastic versions of the basic model are described and analysed. For both versions of the model we show that assuming a uniform susceptible population, with average susceptibility, leads to an increased spread of infection. We also show how our results can be extended to the carrier-borne epidemic model of Weiss (1965).

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