Codynamics of Four Variables Involved in Dengue Transmission and Its Control by Community Intervention: A System of Four Difference Equations

In the case of Dengue transmission and control, the interaction of nature and society is captured by a system of difference equations. For the purpose of studying the dynamics of these interactions, four variables involved in a Dengue epidemic: proportion of infected people (P), number of mosquitoes involved in transmission (M), mosquito habitats (H) and population awareness (A), are linked in a system of difference equations: [equation omitted]. The constraints have socio-ecological meaning. The initial conditions are such that 0 P0 1; (M0;H0;A0) (0; 0; 0), the parameters l,a, c, r 2 (0; 1), and the parameters f, i, b and p are positive. The paper is concerned with the analysis of solutions of the above system for p = q. We studied the global asymptotic stability of the degenerate equilibrium. We also propose extensions of the above model and some open problems. We explored the role of memory in community awareness by numerical simulations. When the memory parameter is large, the proportion of infected people decreases and stabilizes at zero. Below a critical point we observe periodic oscillations

Spatial Spread of Tuberculosis through Neighborhoods Segregated by Socioeconomic Position: A Stochastic Automata Model

Transmission of the agent of tuberculosis, Mycobacterium tuberculosis, is dependent on social context. A discrete spatial model representing neighborhoods segregated by levels of crowding and immunocompetence is constructed and used to evaluate prevention strategies, based on a number of assumptions about the spatial dynamics of tuberculosis. A cellular automata model is used to (a) construct neighborhoods of different densities, (b) model stochastically local interactions among individuals, and (c) model the spread of tuberculosis within and across neighborhoods over time. Since infected people may become progressively sick but also heal through treatment, the transition among stages was modeled with transition probabilities. A moderate level of successful treatment (40%) dramatically reduced the number of infections across all neighborhoods. Increasing the treatment in neighborhoods of a lower socioeconomic level from 40% to 90% results in an additional decrease of approximately 25% in the number of infected individuals overall. In conclusion, we find that a combination of a moderate level of successful treatment across all areas with more focused treatment efforts in lower socioeconomic areas resulted in the least number of infections over time

Spatial Spread of Tuberculosis through Neighborhoods Segregated by Socioeconomic Position: A Stochastic Automata Model

Transmission of the agent of tuberculosis, Mycobacterium tuberculosis, is dependent on social context. A discrete spatial model representing neighborhoods segregated by levels of crowding and immunocompetence is constructed and used to evaluate prevention strategies, based on a number of assumptions about the spatial dynamics of tuberculosis. A cellular automata model is used to (a) construct neighborhoods of different densities, (b) model stochastically local interactions among individuals, and (c) model the spread of tuberculosis within and across neighborhoods over time. Since infected people may become progressively sick but also heal through treatment, the transition among stages was modeled with transition probabilities. A moderate level of successful treatment (40%) dramatically reduced the number of infections across all neighborhoods. Increasing the treatment in neighborhoods of a lower socioeconomic level from 40% to 90% results in an additional decrease of approximately 25% in the number of infected individuals overall. In conclusion, we find that a combination of a moderate level of successful treatment across all areas with more focused treatment efforts in lower socioeconomic areas resulted in the least number of infections over time