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

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.Comment: This is a preprint of a paper whose final and definite form is with 'Chaos, Solitons & Fractals', available from [http://www.elsevier.com/locate/issn/09600779]. Submitted 23-July-2018; Revised 14-Oct-2018; Accepted 15-Oct-2018. arXiv admin note: substantial text overlap with arXiv:1801.0963

Did Neoliberalizing West African Forests Produce a New Niche for Ebola?

A recent study introduced a vaccine that controls Ebola Makona, the Zaire ebolavirus variant that has infected 28,000 people in West Africa. We propose that even such successful advances are insufficient for many emergent diseases. We review work hypothesizing that Makona, phenotypically similar to much smaller outbreaks, emerged out of shifts in land use brought about by neoliberal economics. The epidemiological consequences demand a new science that explicitly addresses the foundational processes underlying multispecies health, including the deep-time histories, cultural infrastructure, and global economic geographies driving disease emergence. The approach, for instance, reverses the standard public health practice of segregating emergency responses and the structural context from which outbreaks originate. In Ebola's case, regional neoliberalism may affix the stochastic "friction" of ecological relationships imposed by the forest across populations, which, when above a threshold, keeps the virus from lining up transmission above replacement. Export-led logging, mining, and intensive agriculture may depress such functional noise, permitting novel spillovers larger forces of infection. Mature outbreaks, meanwhile, can continue to circulate even in the face of efficient vaccines. More research on these integral explanations is required, but the narrow albeit welcome success of the vaccine may be used to limit support of such a program.SCOPUS: re.jinfo:eu-repo/semantics/publishe

Did Ebola emerge in West Africa by a policy-driven phase change in agroecology? Ebola's social context

SCOPUS: no.jinfo:eu-repo/semantics/publishe

Applied mathematical modelling with new parameters and applications to some real life problems

Some Epidemic models with fractional derivatives were proved to be well-defined, well-posed and more accurate [34, 51, 116], compared to models with the conventional derivative. An Ebola epidemic model with non-linear transmission is fully analyzed. The model is expressed with the conventional time derivative with a new parameter included, which happens to be fractional (that derivative is called the derivative). We proved that the model is well-de ned and well-posed. Moreover, conditions for boundedness and dissipativity of the trajectories are established. Exploiting the generalized Routh-Hurwitz Criteria, existence and stability analysis of equilibrium points for the Ebola model are performed to show that they are strongly dependent on the non-linear transmission. In particular, conditions for existence and stability of a unique endemic equilibrium to the Ebola system are given. Numerical simulations are provided for particular expressions of the non-linear transmission, with model's parameters taking di erent values. The resulting simulations are in concordance with the usual threshold behavior. The results obtained here may be signi cant for the ght and prevention against Ebola haemorrhagic fever that has so far exterminated hundreds of families and is still a ecting many people in West-Africa and other parts of the world. The full comprehension and handling of the phenomenon of shattering, sometime happening during the process of polymer chain degradation [129, 142], remains unsolved when using the traditional evolution equations describing the degradation. This traditional model has been proved to be very hard to handle as it involves evolution of two intertwined quantities. Moreover, the explicit form of its solution is, in general, impossible to obtain. We explore the possibility of generalizing evolution equation modeling the polymer chain degradation and analyze the model with the conventional time derivative with a new parameter. We consider the general case where the breakup rate depends on the size of the chain breaking up. In the process, the alternative version of Sumudu integral transform is used to provide an explicit form of the general solution representing the evolution of polymer sizes distribution. In particular, we show that this evolution exhibits existence of complex periodic properties due to the presence of cosine and sine functions governing the solutions. Numerical simulations are performed for some particular cases and prove that the system describing the polymer chain degradation contains complex and simple harmonic poles whose e ects are given by these functions or a combination of them. This result may be crucial in the ongoing research to better handle and explain the phenomenon of shattering. Lastly, it has become a conjecture that power series like Mittag-Le er functions and their variants naturally govern solutions to most of generalized fractional evolution models such as kinetic, di usion or relaxation equations. The question is to say whether or not this is always true! Whence, three generalized evolution equations with an additional fractional parameter are solved analytically with conventional techniques. These are processes related to stationary state system, relaxation and di usion. In the analysis, we exploit the Sumudu transform to show that investigation on the stationary state system leads to results of invariability. However, unlike other models, the generalized di usion and relaxation models are proven not to be governed by Mittag-Le er functions or any of their variants, but rather by a parameterized exponential function, new in the literature, more accurate and easier to handle. Graphical representations are performed and also show how that parameter, called ; can be used to control the stationarity of such generalized models.Mathematical SciencesPh. D. (Applied Mathematics

Epidemiological Analysis of Symmetry in Transmission of the Ebola Virus with Power Law Kernel

This study presents a mathematical model of non-integer order through the fractal fractional Caputo operator to determine the development of Ebola virus infections. To construct the model and conduct analysis, all Ebola virus cases are taken as incidence data. A symmetric approach is utilized for qualitative and quantitative analysis of the fractional order model. Additionally, stability is evaluated, along with the local and global effects of the virus that causes Ebola. Using the fractional order model of Ebola virus infections, the existence and uniqueness of solutions, as well the posedness and biological viability and disease free equilibrium points are confirmed. Many applications of fractional operators in modern mathematics exist, including the intricate and important study of symmetrical systems. Symmetry analysis is a powerful tool that enables the creation of numerical solutions for a given fractional differential equation very methodically. For this, we compare the results with the Caputo derivative operator to understand the dynamic behavior of the disease. The simulation demonstrates how all classes have convergent characteristics and maintain their places over time, reflecting the true behavior of Ebola virus infection. Power law kernel with the two step polynomial Newton method were used. This model seems to be quite strong and capable of reproducing the issue’s anticipated theoretical conditions.Basque Government:Grant IT1555-22 Basque Government: Grant KK-2022/00090 MCIN/AEI 269.10.13039/501100011033/FEDER,UE: Grant PID2021-1235430B-C21 MCIN/AEI 269.10.13039/501100011033/FEDER,UE: Grant PID2021-1235430B-C22

On Some Compartmental Models for Ebola Disease

In this paper, we consider an epidemic model of Ebola disease which is deadly in its transmission. Local stability analysis of the model equilibria was investigated. We computed the basic reproduction number 〖 R〗_0 using the next generation method. The threshold parameter R_0 was found to be dependent on several hosts of model parameters in determining the stability of an invading epidemic into the population. We have numerically described the model trajectories using Matlab. KEYWORDS: Basic Reproduction number, Ebola virus, Next-generation matrix, Local stability analysis

Some Remarks about the Complexity of Epidemics Management

Recent outbreaks of Ebola, H1N1 and other infectious diseases have shown that the assumptions underlying the established theory of epidemics management are too idealistic. For an improvement of procedures and organizations involved in fighting epidemics, extended models of epidemics management are required. The necessary extensions consist in a representation of the management loop and the potential frictions influencing the loop. The effects of the non-deterministic frictions can be taken into account by including the measures of robustness and risk in the assessment of management options. Thus, besides of the increased structural complexity resulting from the model extensions, the computational complexity of the task of epidemics management - interpreted as an optimization problem - is increased as well. This is a serious obstacle for analyzing the model and may require an additional pre-processing enabling a simplification of the analysis process. The paper closes with an outlook discussing some forthcoming problems

Ebola epidemic model with dynamic population and memory

The recent outbreaks of Ebola encourage researchers to develop mathematical models for simulating the dynamics of Ebola transmission. We continue the study of the models focusing on those with a variable population. Hence, this paper presents a compartmental model consisting of 8-dimensional nonlinear dif- ferential equations with a dynamic population and investigates its basic reproduction number. Moreover, a dimensionless model is introduced for numerical analysis, thus proving the disease-free equilibrium is locally asymptotically stable whenever the threshold condition, known as a basic reproduction number, is less than one. Finally, we use a fractional differential form of the model to sufficiently fit long time-series data of Guinea, Liberia, and Sierra Leone retrieved from the World Health Organization, and the numerical results demonstrate the performance of the model.publishe