In wireless sensor networks energy is a very important issue because these networks consist of lowpower sensor nodes. This paper proposes a new protocol to reach energy efficiency. The protocol has a different priority in energy efficiency as reducing energy consumption in nodes, prolonging lifetime of the whole network, increasing system reliability, increasing the load balance of the network, and reducing packet delays in the network. In the new protocol is proposed an intelligent routing protocol algorithm. It is based on reinforcement learning techniques. In the first step of the protocol, a new clustering method is applied to the network and the network is established using a connected graph. Then data is transmitted using the -value parameter of reinforcement learning technique. The simulation results show that our protocol has improvement in different parameters such as network lifetime, packet delivery, packet delay, and network balance.

A wireless sensor network (WSN) is a collection of sensor nodes that dynamically self-organize themselves into a wireless network without the utilization of any preexisting infrastructure. One of the major problems in WSNs is the energy consumption, whereby the network lifetime is dependent on this factor. In this paper, we propose an optimal routing protocol for WSN inspired by the foraging behavior of ants. The ants try to find existing paths between the source and base station. Furthermore, we have combined this behavior of ants with fuzzy logic in order for the ants to make the best decision. In other words, the fuzzy logic is applied to make the use of these paths optimal. Our algorithm uses the principles of the fuzzy ant colony optimization routing (FACOR) to develop a suitable problem solution. The performance of our routing algorithm is evaluated by Network Simulator 2 (NS2). The simulation results show that our algorithm optimizes the energy consumption amount, decreases the number of routing request packets, and increases the network lifetime in comparison with the original AODV.

The purpose of this paper is to investigate the transmission dynamics of a fractional-order mathematical model of COVID-19 including susceptible ($$\textsc {S}$$ S ), exposed ($$\textsc {E}$$ E ), asymptomatic infected ($$\textsc {I}_1$$ I 1 ), symptomatic infected ($$\textsc {I}_2$$ I 2 ), and recovered ($$\textsc {R}$$ R ) classes named $$\mathrm {SEI_{1}I_{2}R}$$ SEI 1 I 2 R model, using the Caputo fractional derivative. Here, $$\mathrm {SEI_{1}I_{2}R}$$ SEI 1 I 2 R model describes the effect of asymptomatic and symptomatic transmissions on coronavirus disease outbreak. The existence and uniqueness of the solution are studied with the help of Schaefer- and Banach-type fixed point theorems. Sensitivity analysis of the model in terms of the variance of each parameter is examined, and the basic reproduction number $$(R_{0})$$ ( R 0 ) to discuss the local stability at two equilibrium points is proposed. Using the Routh–Hurwitz criterion of stability, it is found that the disease-free equilibrium will be stable for $$R_{0} < 1$$ R 0 < 1 whereas the endemic equilibrium becomes stable for $$R_{0} > 1$$ R 0 > 1 and unstable otherwise. Moreover, the numerical simulations for various values of fractional-order are carried out with the help of the fractional Euler method. The numerical results show that asymptomatic transmission has a lower impact on the disease outbreak rather than symptomatic transmission. Finally, the simulated graph of total infected population by proposed model here is compared with the real data of second-wave infected population of COVID-19 outbreak in India.

In this manuscript, a qualitative analysis of the mathematical model of novel coronavirus ( -19) involving anew devised fractal-fractional operator in the Caputo sense having the fractional-order and the fractal dimension is considered. The concerned model is composed of eight compartments: susceptible, exposed, infected, super-spreaders, asymptomatic, hospitalized, recovery and fatality. Under the new derivative the existence and uniqueness of the solution for considered model are proved using Schaefer’s and Banach type fixed point approaches. Additionally, with the help of nonlinear functional analysis, the condition for Ulam’s type of stability of the solution to the considered model is established. For numerical simulation of proposed model, a fractional type of two-step Lagrange polynomial known as fractional Adams-Bashforth method is applied to simulate the results. At last, the results are tested with real data from -19 outbreak in Wuhan City, Hubei Province of China from 4 January to 9 March 2020, taken from a source [42] . The Numerical results are presented in terms of graphs for different fractional-order and fractal dimensions to describe the transmission dynamics of disease infection.

In this paper, new model on novel coronavirus disease ([Formula: see text]-19) with four compartments including susceptible, exposed, infected, and recovered class with fractal-fractional derivative is proposed. Here, Banach and Leray–Schauder alternative type theorems are used to establish some appropriate conditions for the existence and uniqueness of the solution. Also, stability is needed in respect of the numerical solution. Therefore, Ulam–Hyers stability using nonlinear functional analysis is used for the proposed model. Moreover, the numerical simulation using the technique of fundamental theorem of fractional calculus and the two-step Lagrange polynomial known as fractional Adams-Bashforth [Formula: see text] method is proposed. The obtained results are tested on real data of [Formula: see text]-19 outbreak in Malaysia from 25 January till 10 May 2020. The numerical simulation of the proposed model has performed in terms of graphs for different fractional-order [Formula: see text] and fractal dimensions [Formula: see text] via number of considered days of disease spread in Malaysia. Since [Formula: see text]-19 transmits rapidly, perhaps, the clear understanding of transmission dynamics of [Formula: see text]-19 is important for countries to implement suitable strategies and restrictions such as Movement Control Order (MCO) by the Malaysian government, against the disease spread. The simulated results of the presented model demonstrate that movement control order has a great impact on the transmission dynamics of disease outbreak in Malaysia. It can be concluded that by adopting precautionary measures as restrictions on individual movement the transmission of the disease in society is reduced. In addition, for such type of dynamical study, fractal-fractional calculus tools may be used as powerful tools to understand and predict the global dynamics of the mentioned disease in other countries as well.