Mathematical model of Zika virus with vertical transmission

Zika is a flavivirus transmitted to humans through either the bites of infected Aedes mosquitoes or sexual transmission. Zika has been linked to congenital anomalies such as microcephaly. In this paper, we analyze a new system of ordinary differential equations which incorporates human vertical transmission of Zika virus, the birth of babies with microcephaly and asymptomatically infected individuals. The Zika model is locally and globally asymptotically stable when the basic reproduction number is less than unity. Our model shows that asymptomatic individuals amplify the disease burden in the community, and the most important parameters for ZIKV spread are the death rate of mosquitoes, the mosquito biting rate, the mosquito recruitment rate, and the transmission per contact to mosquitoes and to adult humans. Scenario exploration indicates that personal-protection is a more effective control strategy than mosquito-reduction strategy. It also shows that delaying conception reduces the number of microcephaly cases, although this does little to prevent Zika transmission in the broader community. However, by coupling aggressive vector control and personal protection use, it is possible to reduce both microcephaly and Zika transmission. 2000 Mathematics Subject Classifications: 92B05, 93A30, 93C15

Mathematical Modeling for Studying the Sustainability of Plants Subject to the Stress of Two Distinct Herbivores

Viability of plants, especially endangered species, are usually affected by multiple stressors, including insects, herbivores, environmental factors and other plant species. We present new mathematical models, based on systems of ordinary differential equations, of two distinct herbivore species feeding (two stressors) on the same plant species. The new feature is the explicit functional form modeling the simultaneous feedback interactions (synergistic or additive or antagonistic) between the three species in the ecosystem. The goal is to investigate whether the coexistence of the plant and both herbivore species is possible (a sustainable system) and under which conditions sustainability is feasible. Our theoretical analysis of the novel model without including competitions among the two herbivores reveals that the number of equilibrium states and their local stability depends on the type of interaction between the stressors: synergistic or additive or antagonistic. Our numerical results, based on value of parameters available, suggest that a sustainable system requires significant herbivore inter- or intra-species competition or both types. Additionally, our numerical findings indicate that competition and interaction of additive type promotes coexistence equilibrium states with the highest plant biomass. Furthermore, the system can exhibit periodic behavior and show the potential for multi-stability

Geochemistry of fluid discharges from Peteroa volcano (Argentina-Chile) in 2010-2015: Insights into compositional changes related to the fluid source region(s).

This study presents the first geochemical data of fluid discharges collected from February 2010 to March 2015 from the Planchon-Peteroa-Azufre Volcanic Complex (PPAVC), located in the Transitional Southern Volcanic Zone (TSVZ) at the border between Argentina and Chile. During the study period, from January 2010 to July 2011, Peteroa volcano experienced phreatic to phreatomagmatic eruption possibly related to the devastating Maule earthquake occurred on February 27, 2010. The compositional dataset includes low temperature (from 43.2 to 102 degrees C) gas discharges from (i) the summit of Peteroa volcano and (ii) the SE flank of Azufre volcano, both marked by a significant magmatic fluid contribution, as well as bubbling gases located at the foothill of the Peteroa volcanic edifice, which showed a chemical signature typical of hydrothermal fluids. In 2012, strong compositional changes affected the Peteroa gases from the summit area: the acidic gas species, especially SO2, increased, suggesting an input of fluids from magma degassing. Nevertheless, the R/Ra and delta C-13-CO2 values decreased, which would imply an enhanced contribution from a meteoric-hydrothermal source. In 2014-2015, the chemical and isotopic compositions of the 2010-2011 gases were partially restored. The anomalous decoupling between the chemical and the isotopic parameters was tentatively interpreted as produced by degassing activity from a small batch of dacitic magma that in 2012 masked the compositional signature of the magmatic fluids released from a basaltic magma that dominated the gas chemistry in 2010-2011. This explanation reliably justifies the observed geochemical data, although the mechanisms leading to the change in time of the dominating magmatic fluid source are not clear. At this regard, a geophysical survey able to provide information on the location of the two magma batches could be useful to clarify the possible relationships between the compositional changes that affected the Peteroa fluid discharges and the 2010-2011 eruptive activity.FONDECYT Iniciacion Project 11100372 FONDAP "Centro de Excelencia en Geotermia de los Andes" 15090013 Universidad de Buenos Aires UBACyT 20020120300077BA IDEAN institute (UBA-CONICET) Laboratory of Fluid and Rock Geochemistry of the Department of Earth Sciences (Florence, Italy

Assessment of optimal strategies in a two-patch dengue transmission model with seasonality

Emerging and re-emerging dengue fever has posed serious problems to public health officials in many tropical and subtropical countries. Continuous traveling in seasonally varying areas makes it more difficult to control the spread of dengue fever. In this work, we consider a two-patch dengue model that can capture the movement of host individuals between and within patches using a residence-time matrix. A previous two-patch dengue model without seasonality is extended by adding host demographics and seasonal forcing in the transmission rates. We investigate the effects of human movement and seasonality on the two-patch dengue transmission dynamics. Motivated by the recent Peruvian dengue data in jungle/rural areas and coast/urban areas, our model mimics the seasonal patterns of dengue outbreaks in two patches. The roles of seasonality and residence-time configurations are highlighted in terms of the seasonal reproduction number and cumulative incidence. Moreover, optimal control theory is employed to identify and evaluate patch-specific control measures aimed at reducing dengue prevalence in the presence of seasonality. Our findings demonstrate that optimal patch-specific control strategies are sensitive to seasonality and residence-time scenarios. Targeting only the jungle (or endemic) is as effective as controlling both patches under weak coupling or symmetric mobility. However, focusing on intervention for the city (or high density areas) turns out to be optimal when two patches are strongly coupled with asymmetric mobility.ope

Mathematical Model of MDR-TB and XDR-TB with Isolation and Lost to Follow-Up

We present a deterministic model with isolation and lost to follow-up for the transmission dynamics of three strains of Mycobacterium tuberculosis (TB), namely, the drug sensitive, multi-drug-resistant (MDR), and extensively-drug-resistant (XDR) TB strains. The model is analyzed to gain insights into the qualitative features of its associated equilibria. Some of the theoretical and epidemiological findings indicate that the model has locally asymptotically stable (LAS) disease-free equilibrium when the associated reproduction number is less than unity. Furthermore, the model undergoes in the presence of disease reinfection the phenomenon of backward bifurcation, where the stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the associated reproduction number is less than unity. Further analysis of the model indicates that the disease-free equilibrium is globally asymptotically stable (GAS) in the absence of disease reinfection. The result of the global sensitivity analysis indicates that the dominant parameters are the disease progression rate, the recovery rate, the infectivity parameter, the isolation rate, the rate of lost to follow-up, and fraction of fast progression rates. Our results also show that increase in isolation rate leads to a decrease in the total number of individuals who are lost to follow-up