Abstract
The spread of epidemics has been extensively investigated using susceptible-exposed infectious-recovered-susceptible (SEIRS) models. In this work, we propose a SEIRS pandemic model with infection forces and intervention strategies. The proposed model is characterized by a stochastic differential equation (SDE) framework with arbitrary parameter settings. Based on a Markov semigroup hypothesis, we demonstrate the effect of the proliferation number R0S on the SDE solution. On the one hand, when R0S < 1, the SDE has an illness-free solution set under gentle additional conditions. This implies that the epidemic can be eliminated with a likelihood of 1. On the other hand, when R0S > 1, the SDE has an endemic stationary circulation under mild additional conditions. This prompts the stochastic regeneration of the epidemic. Also, we show that arbitrary fluctuations can reduce the infection outbreak. Hence, valuable procedures can be created to manage and control epidemics.
Highlights
Mummert and Otunuga [22] adapted generalized method of moments to identify the time-dependent disease transmission rate and time-dependent noise for the stochastic susceptible- exposed- infectious- temporarily immune- susceptible disease model (SEIRS) with vital rates. e stochasticity appears in the model due to fluctuations in the time-dependent transmission rate of the disease. e method is demonstrated with the US influenza data from 2004-2005 through 2016-2017 influenza seasons. e transmission rate and noise intensity stochastically work together to generate the yearly peaks in infections. ere has been much work already done on the stochastic aspects of the epidemic model
We consider a pandemic of the SEIR type, where we indicate the numbers of susceptible, exposed, infectious, and recovered people by S, E, I, and R, respectively. e total population N is given by N S + E + I + R. e SEIR model accepts that the recovered people might lose their immunity and reemerge in the susceptible state. e SEIR model is applicable to numerous infectious epidemics such as H7N9, bacterial loose bowels, typhoid fever, measles, dengue fever, and AIDS [21, 22, 27]
For the convenience of display, the simulation is set as 100 times 100 in the space-time range, the abscissa represents the time, and the ordinate represents the number of patients. e simulations can help us to investigate how the ecological perturbations and the harmfully idle periods influence the spread of epidemics
Summary
Many biological and human populations have been facing the threat of viral epidemics. e spread of such epidemics typically leads to large death tolls and significant economic and healthcare costs. e Ebola outbreak in early 2014 led to the loss of thousands of lives in Africa [1,2,3]. ousands of people died as victims of SARS in early 2002 [4,5,6,7]. e H7N9 [8,9,10,11] and H5N6 [12, 13] epidemics emerge every year in southern areas of China, causing excessive poultry losses. Dalal et al [26] introduced stochasticity into a deterministic model of internal HIV viral dynamics via the same technique of parameter perturbation into the death rate of healthy cells, infected cells, and viral particles. Another way to introduce stochasticity into deterministic models is telegraph noise where the parameters switch from one set to another according to a Markov switching process. The main contributions are introducing a susceptible-exposed-infectious-recovered-susceptible (SEIRS) epidemic model with infection forces and investigating how changes in conditions, hatching time, and other parameter settings affect the epidemic dynamics.
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