On the Dynamics of Dengue Virus type 2 with Residence Times and Vertical Transmission

A two-patch mathematical model of Dengue virus type 2 (DENV-2) that accounts for vectors' vertical transmission and between patches human dispersal is introduced. Dispersal is modeled via a Lagrangian approach. A host-patch residence-times basic reproduction number is derived and conditions under which the disease dies out or persists are established. Analytical and numerical results highlight the role of hosts' dispersal in mitigating or exacerbating disease dynamics. The framework is used to explore dengue dynamics using, as a starting point, the 2002 outbreak in the state of Colima, Mexico

Effect of General Cross-Immunity Protection and Antibody- Dependent Enhancement in Dengue Dynamics

A mathematical model to describe the dynamic of a multiserotype infectious disease at the population level is studied. Applied to dengue fever epidemiology, we analyse a mathematical model with time delay to describe the cross-immunity protection period, including a key parameter for the antibody-dependent enhancement (ADE) effect, the well-known features of dengue fever infection. Numerical experiments are performed to show the stability of the coexistence equilibrium, which is completely determined by the basic reproduction number and by the invasion reproduction number, as well as the bifurcation structures for different scenarios of dengue fever transmission in a population. The model shows a rich dynamical behavior, from fixed points and periodic oscillations up to chaotic behaviour with complex attractors.Laboratory for Industrial and Applied Mathematics (LIAM), Department of Mathematics and Statistics, York University, CA

Numerical Analytic Solution of SIR Model of Dengue Fever Disease in South Sulawesi using Homotopy Perturbation Method and Variational Iteration Method

In this research, the susceptible"“infected"“recovered (SIR) model of dengue fever is considered. We have implemented two analytical techniques, namely the variational iteration method (VIM) and the homotopy perturbation method (HPM) for solving the SIR model. The Lagrange multiplier was investigated for the VIM and He's polynomial approach for the HPM was used. In these schemes, the solution takes the form of a convergent series with easily computable components. The resultsshow thatthe VIM solution is more accurate than the HPM solution for short time intervals, whereasthe HPM is more accurate than the VIM for long time intervalswhencompared with the fourth-orderRunge-Kutta method (RK4).We found that the HPM and the RK4 were in excellent conformance

Cross immunity protection and antibody-dependent enhancement in a distributed delay dynamic model

Dengue fever is endemic in tropical and subtropical countries, and certain important features of the spread of dengue fever continue to pose challenges for mathematical modelling. Here we propose a system of integro-differential equations (IDE) to study the disease transmission dynamics that involve multi-serotypes and cross immunity. Our main objective is to incorporate and analyze the effect of a general time delay term describing acquired cross immunity protection and the effect of antibody-dependent enhancement (ADE), both characteristics of Dengue fever. We perform qualitative analysis of the model and obtain results to show the stability of the epidemiologically important steady solutions that are completely determined by the basic reproduction number and the invasion reproduction number. We establish the global dynamics by constructing a suitable Lyapunov functional. We also conduct some numerical experiments to illustrate bifurcation structures, indicating the occurrence of periodic oscillations for a specific range of values of a key parameter representing ADE.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brazil (CAPES) - Finance Code 001 LIAM - Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University-CA

Research on Multi-Agent Simulation of Epidemic News Spread Characteristics

The spread of news about an epidemic can easily lead to a social panic. In order to devise measures to control such a panic, it is necessary to consider characteristics of the spread of epidemic news, based on mechanisms at the individual level. In this paper, first, some features of multi-agent simulation are reviewed. Then a multi-agent simulation model of epidemic news spread (ENS) is designed and realized. Based on simulation experiments and sensitivity analyses, the influence of social relationships, the degree of trust in news of the epidemic, the epidemic spread intensity and the network structure of the epidemic news spread are studied. The research results include: (1) As the number of social relationships increases, the rate of spread of epidemic news rapidly rises, and the ratio of people who have heard the news directly decreases. The result is that the \'radiation effect\' of the epidemic news spread will be enhanced when the number of social relationships increases. (2) With the increase of the degree of trust in the news, the rate of spread of the news will also rapidly increase, but variation in the ratio of the people who have heard the news directly is not significant. This means that the \'radiation effect\' of the spread of the news does not change much more in relation to the degree of trust in the epidemic news. (3) The ratio of the people who have heard the news directly increases when the infection range increases (i.e. the spread intensity of epidemic increases), and vice versa. But the variation of the speed of the epidemic news spread is not significant. (4) When the network structure is assumed to be a small world network, the spread speed will be slower than that in a random network with the same average vertex degree and the forgetting speed will be faster than that in a random network with the same average vertex degree.Multi-Agent Simulation, News Spread, Small World Network , Epidemic

A model of dengue fever

BACKGROUND: Dengue is a disease which is now endemic in more than 100 countries of Africa, America, Asia and the Western Pacific. It is transmitted to the man by mosquitoes (Aedes) and exists in two forms: Dengue Fever and Dengue Haemorrhagic Fever. The disease can be contracted by one of the four different viruses. Moreover, immunity is acquired only to the serotype contracted and a contact with a second serotype becomes more dangerous. METHODS: The present paper deals with a succession of two epidemics caused by two different viruses. The dynamics of the disease is studied by a compartmental model involving ordinary differential equations for the human and the mosquito populations. RESULTS: Stability of the equilibrium points is given and a simulation is carried out with different values of the parameters. The epidemic dynamics is discussed and illustration is given by figures for different values of the parameters. CONCLUSION: The proposed model allows for better understanding of the disease dynamics. Environment and vaccination strategies are discussed especially in the case of the succession of two epidemics with two different viruses