Narrow Results

Hantavirus outbreaks in the American Southwest are hypothesized to be driven by episodic seasonal events of high precipitation, promoting rapid increases in virus-reservoir rodent species that then move across the landscape from high quality montane forested habitats (refugia), eventually over-running human residences and increasing disease risk. In this study, the velocities of rodents and virus diffusion wave propagation and retraction were documented and quantified in the sky-islands of northern New Mexico and related to rodent-virus relationships in refugia versus nonrefugia habitats. Deer mouse (Peromyscus maniculatus) refugia populations exhibited higher Sin Nombre Virus (SNV) infection prevalence than nonrefugia populations. The velocity of propagating diffusion waves of Peromyscus from montane to lower grassland habitats was measured at $24.6\pm 5.6$ m/day (SE), with wave retraction velocities of $28\pm 8.4$ m/day. SNV infection diffusion wave propagation velocity within a deer mouse population averaged $27.5\pm 7.8$ m/day, with a faster retraction wave velocity of $161.5\pm 80.7$ m/day. A spatio-temporal analysis of human Hantavirus Pulmonary Syndrome (HPS) cases during the initial 1993 epidemic revealed a positive linear relationship between the time during the epidemic and the distance of human cases from the nearest deer mouse refugium, with a landscape diffusion wave velocity of $19.6\pm 1.0$ m/day ($r^2=0.96$). These consistent diffusion propagation wave velocity results support the traveling wave component of the HPS outbreak theory and can provide information on space–time constraints for future outbreak forecasts.

In this paper, we have investigated women’s malignant disease, cervical cancer, by constructing the compartmental model. An extended fractal–fractional model is used to study the disease dynamics. The points of equilibria are computed analytically and verified by numerical simulations. The key role of $R_0$ in describing the stability of the model is presented. The sensitivity analysis of $R_0$ for deciding the role of certain parameters altering the disease dynamics is carried out. The numerical simulations of the proposed numerical technique are demonstrated to test the claimed facts.