Travelling waves for an epidemic model with non-smooth treatment rates

This is the post-print version of the final published paper that is available from the link below. Copyright @ 2010 IOP Publishing Ltd and SISSA.We consider a susceptible–infected–removed (SIR) epidemic model with two types of nonlinear treatment rates: (i) piecewise linear treatment rate with saturation effect, (ii) piecewise constant treatment rate with a jump (Heaviside function). For case (i), we compute travelling front solutions whose profiles are heteroclinic orbits which connect either the disease-free state to an infective state or two endemic states with each other. For case (ii), it is shown that the profile has the following properties: the number of susceptibles is monotonically increasing and the number of infectives approaches zero at infinity, while their product converges to a constant. Numerical simulations are performed for all these cases. Abnormal behaviour like travelling waves with non-monotonic profile or oscillations is observed

Mitigating Epidemics through Mobile Micro-measures

Epidemics of infectious diseases are among the largest threats to the quality of life and the economic and social well-being of developing countries. The arsenal of measures against such epidemics is well-established, but costly and insufficient to mitigate their impact. In this paper, we argue that mobile technology adds a powerful weapon to this arsenal, because (a) mobile devices endow us with the unprecedented ability to measure and model the detailed behavioral patterns of the affected population, and (b) they enable the delivery of personalized behavioral recommendations to individuals in real time. We combine these two ideas and propose several strategies to generate such recommendations from mobility patterns. The goal of each strategy is a large reduction in infections, with a small impact on the normal course of daily life. We evaluate these strategies over the Orange D4D dataset and show the benefit of mobile micro-measures, even if only a fraction of the population participates. These preliminary results demonstrate the potential of mobile technology to complement other measures like vaccination and quarantines against disease epidemics.Comment: Presented at NetMob 2013, Bosto

Mathematical Modelling of Transmission Dynamics of Anthrax in Human and Animal Population.

Anthrax is an infectious disease that can be categorised under zoonotic diseases. It is caused by the bacteria known as Bacillus anthraces. Anthrax is one of the most leading causes of deaths in domestic and wild animals. In this paper, we develop and investigated a mathematical model for the transmission dynamics of the disease. Ordinary differential equations were formulated from the mathematical model. We performed the quantitative and qualitative analysis of the model to explain the transmission dynamics of the anthrax disease. We analysed and determined the model’s steady states solutions. The disease-free equilibrium of the anthrax model is analysed for locally asymptotic stability and the associated epidemic basic reproduction number. The model’s disease free equilibrium has shown to be locally asymptotically stable when the basic reproductive number is less than unity. The model is found to exhibit the existence of multiple endemic equilibria. Sensitivity analysis was performed on the model’s parameters to investigate the most sensitive parameters in the dynamics of the diseases. Keywords: Anthrax model, Basic reproductive number, Asymptotic stability, Endemic equilibrium, Sensitivity analysis

Optimal Campaign in the Smoking Dynamics

We present the optimal campaigns in the smoking dynamics. Assuming that the giving up smoking model is described by the simplified PLSQ (potential-light-smoker-quit smoker) model, we consider two possible control variables in the form of education and treatment campaigns oriented to decrease the attitude towards smoking. In order to do this we minimize the number of light (occasional) and persistent smokers and maximize the number of quit smokers in a community. We first show the existence of an optimal control for the control problem and then derive the optimality system by using the Pontryagin maximum principle. Finally numerical results of real epidemic are presented to show the applicability and efficiency of this approach

Numerical Solution and Analysis for Acute and Chronic Hepatitis B

In this article, we present the transmission dynamic of the acute and chronic hepatitis B epidemic problem to control the spread of hepatitis B in a community. In order to do this, first we present sensitivity analysis of the basic reproduction number R0. We develop a unconditionally convergent nonstandard finite difference scheme by applying Mickens approach φ(h) = h + O(h^2) instead of h to control the spread of this infection, treatment and vaccination to minimize the number of acute infected, chronically infected with hepatitis B individuals and maximize the number of susceptible and recovered individuals. The stability analysis of the scheme has been developed by theorems which shows the both stable locally and globally. Comparison is also made with standard nonstandard finite difference scheme. Finally numerical simulations are also established to investigate the influence of the system parameter on the spread of the disease

Beyond just “flattening the curve”: Optimal control of epidemics with purely non-pharmaceutical interventions

When effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, home quarantine and far-reaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR (susceptible-exposed-infectious-recovered) model and continuous-time optimal control theory, we compute the optimal non-pharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible. In this case, the optimal control must meet competing requirements: First, the minimization of disease-related deaths, and, second, the establishment of a sufficient degree of natural immunity at the end of the measures, in order to exclude a second wave. Moreover, the socio-economic costs of the intervention shall be kept at a minimum. The numerically computed optimal control strategy is a single-intervention scenario that goes beyond heuristically motivated interventions and simple “flattening of the curve”. Careful analysis of the computed control strategy reveals, however, that the obtained solution is in fact a tightrope walk close to the stability boundary of the system, where socio-economic costs and the risk of a new outbreak must be constantly balanced against one another. The model system is calibrated to reproduce the initial exponential growth phase of the COVID-19 pandemic in Germany. © 2020, The Author(s)

Beyond just ``flattening the curve'': Optimal control of epidemics with purely non-pharmaceutical interventions

When effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, home quarantine and far-reaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR (susceptible-exposed-infectious-recovered) model and continuous-time optimal control theory, we compute the optimal non-pharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible. In this case, the optimal control must meet competing requirements: First, the minimization of disease-related deaths, and, second, the establishment of a sufficient degree of natural immunity at the end of the measures, in order to exclude a second wave. Moreover, the socio-economic costs of the intervention shall be kept at a minimum. The numerically computed optimal control strategy is a single-intervention scenario that goes beyond heuristically motivated interventions and simple "flattening of the curve". Careful analysis of the computed control strategy reveals, however, that the obtained solution is in fact a tightrope walk close to the stability boundary of the system, where socio-economic costs and the risk of a new outbreak must be constantly balanced against one another. The model system is calibrated to reproduce the initial exponential growth phase of the COVID-19 pandemic in Germany

Threshold Dynamics of a Stochastic S

A stochastic SIR model with vertical transmission and vaccination is proposed and investigated in this paper. The threshold dynamics are explored when the noise is small. The conditions for the extinction or persistence of infectious diseases are deduced. Our results show that large noise can lead to the extinction of infectious diseases which is conducive to epidemic diseases control

A mathematical model for coinfection of listeriosis and anthrax diseases

CITATION: Osman, S. & Makinde, O. D. 2018. A mathematical model for coinfection of listeriosis and anthrax diseases. International Journal of Mathematics and Mathematical Sciences, 2018 (Article ID 1725671), doi:10.1155/2018/1725671.The original publication is available at https://www.hindawi.comListeriosis and Anthrax are fatal zoonotic diseases caused by Listeria monocytogene and Bacillus Anthracis, respectively. In this paper, we proposed and analysed a compartmental Listeriosis-Anthrax coinfection model describing the transmission dynamics of Listeriosis and Anthrax epidemic in human population using the stability theory of differential equations. Our model revealed that the disease-free equilibrium of the Anthrax model only is locally stable when the basic reproduction number is less than one. Sensitivity analysis was carried out on the model parameters in order to determine their impact on the disease dynamics. Numerical simulation of the coinfection model was carried out and the results are displayed graphically and discussed. We simulate the Listeriosis-Anthrax coinfection model by varying the human contact rate to see its effects on infected Anthrax population, infected Listeriosis population, and Listeriosis-Anthrax coinfected population.https://www.hindawi.com/journals/ijmms/2018/1725671/Publisher's versio