Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of the new strain coronavirus COVID-19 to humans. In this paper, we use a stochastic epidemic SIRC model, with cross-immune class and time-delay in transmission terms, for the spread of COVID-19. We analyze the model and prove the existence and uniqueness of positive global solution. We deduce the basic reproduction number 

${\mathcal{R}}_{0}^{s}$
 for the stochastic model which is smaller than 

${\mathcal{R}}_{0}$
 of the corresponding deterministic model. Sufficient conditions that guarantee the existence of a unique ergodic stationary distribution, using the stochastic Lyapunov function, and conditions for the extinction of the disease are obtained. Our findings show that white noise plays an important part in controlling the spread of the disease; When the white noise is relatively large, the infectious diseases will become extinct; Re-infection and periodic outbreaks can occur due to the existence of feedback time-delay (or memory) in the transmission terms.

/pdf/stochastic-sirc-epidemic-model-with-time-delay-for-covid-19-42w8x2w5mm.pdf

Stochastic SIRC epidemic model with time-delay for COVID-19.

We propose a fractional order SIRC epidemic model to describe the dynamics of Salmonella bacterial infection in animal herds. The infection-free and endemic steady sates, of such model, are asymptotically stable under some conditions. The basic reproduction number is calculated, using next-generation matrix method, in terms of contact rate, recovery rate, and other parameters in the model. The numerical simulations of the fractional order SIRC model are performed by Caputo’s derivative and using unconditionally stable implicit scheme. The obtained results give insight to the modelers and infectious disease specialists.

/pdf/on-fractional-sirc-model-with-salmonella-bacterial-infection-sp4kao574l.pdf

On Fractional SIRC Model with Salmonella Bacterial Infection

Global dynamics of a discretized SIRS epidemic model with time delay

This paper deals with the fractional-order SIRC model associated with the evolution of influenza A disease in human population. Qualitative dynamics of the model is determined by the basic reproduction number, R0. We give a detailed analysis for the asymptotic stability of disease-free and positive fixed points. Nonstandard finite difference methods have been used to solve and simulate the system of differential equations.

/pdf/the-fractional-sirc-model-and-influenza-a-3v12njmaav.pdf

The Fractional SIRC Model and Influenza A

A human respiratory syncytial virus surveillance system was implemented in Florida in 1999, to support clinical decision-making for prophylaxis of premature newborns. Recently, a local periodic SEIRS mathematical model was proposed in [Stat. Optim. Inf. Comput. 6 (2018), no. 1, 139–149] to describe real data collected by Florida’s system. In contrast, here we propose a non-local fractional (non-integer) order model. A fractional optimal control problem is then formulated and solved, having treatment as the control. Finally, a cost-effectiveness analysis is carried out to evaluate the cost and the effectiveness of proposed control measures during the intervention period, showing the superiority of obtained results with respect to previous ones.

Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection

Nonstandard numerical methods for a mathematical model for influenza disease

Childhood Obesity in the Region of Valencia, Spain: Evolution and Prevention Strategies

Existence of periodic solutions in a model of respiratory syncytial virus RSV

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Papers

Nonstandard numerical methods for a mathematical model for influenza disease

Childhood Obesity in the Region of Valencia, Spain: Evolution and Prevention Strategies

Existence of periodic solutions in a model of respiratory syncytial virus RSV