Mathematical modelling for Zoonotic Visceral Leishmaniasis dynamics:A new analysis considering updated parameters and notified human Brazilian data

Brazil is one of the highest endemic countries for Zoonotic Visceral Leishmaniasis:according to the Brazilian Ministry of Health,the annual number of new human cases and deaths due to this disease has been increasing for the last 20 years.In addition,regarding the Americas,the specific relationship between canine and human for Visceral Leishmaniasis dynamics is still not well understood.In this work we propose a new model for Zoonotic Visceral Leishmaniasis,based on the models previously published by Burattini et al.(1998)and Ribas et al.(2013).Herein,we modeled the disease dynamics using a modified set of differential equations from those two authors,considering the same assumptions(inclusion of human,dog and sandfly populations,all constants over time).From this set of equations we were able to calculate the basic reproduction number R 0 and to analyze the stability and sensitivity of the system to the parameters variability.As main result,when the stability of the system is reached,the normalized reporting human cases rate is estimated in 9.12E-08/day.This estimation is very close to the 2015 report from Araçatuba city,5.69E-08/day.We also observed from stability and sensitivity analysis that the activity of sandfly population is critical to introduction and maintenance of Zoonotic Visceral Leishmaniasis in the population.In addition,the importance of dog as source of infection concentrates on latent dog,since it does not show clinical symptoms and signs and,therefore,has a great contribution to disease dissemination.As conclusion,considering the presently ethical issues regarding to elimination of positive dog in Brazil and the highly sensitivity of disease dynamics on sandfly population,we recommend that the sandfly population control should be prioritized.

A simple model for COVID-19

An SL1L2I1I2A1A2R epidemic model is formulated that describes the spread of an epidemic in a population.The model incorporates an Erlang distribution of times of sojourn in incubating,symptomatically and asymptomatically infectious compartments.Basic properties of the model are explored,with focus on properties important in the context of current COVID-19 pandemic.

A simple model for fitting mild, severe, and known cases during an epidemic with an application to the current SARSCoV- 2 pandemic

One of the major difficulties with modelling an ongoing epidemic is that often data is limited or incomplete,making it hard to estimate key epidemic parameters and outcomes(e.g.attack rate,peak time,reporting rate,reproduction number).In the current study,we present a model for data-fitting limited infection case data which provides estimates for important epidemiological parameters and outcomes.The model can also provide reasonable short-term(one month)projections.We apply the model to the current and ongoing COVID-19 outbreak in Canada both at the national and provincial/territorial level.

Modelling the HIV persistence through the network of lymphocyte recirculation in vivo

Human Immunodeficiency Virus(HIV)is able to persist in cellular and/or anatomical viral reservoirs,despite the effective inhibition of virus replication by the antiretroviral therapy(ART).Here we develop a mathematical model to gain some insights of HIV persistence relevant to the lymphocyte recirculation network of immune system and the central nervous system(CNS).Our simulations and analyses illustrate the role of the CNS as a virus reservoir to prevent antiretroviral drugs from penetrating the blood-brain(or blood-testis)barrier,and we examine the long-term impact of this reservoir on the transmissibility of an infected individual.We observe numerically that level of HIV in peripheral blood may not accurately reflect the true mechanisms occurring within other organs.

Unraveling the dose-response puzzle of L.monocytogenes:A mechanistic approach

Food-borne disease outbreaks caused by Listeria monocytogenes continue to impose heavy burdens on public health in North America and globally.To explore the threat L.monocytogenes presents to the elderly,pregnant woman and immuno-compromised individuals,many studies have focused on in-host infection mechanisms and risk evaluation in terms of dose-response outcomes.However,the connection of these two foci has received little attention,leaving risk prediction with an insufficient mechanistic basis.Consequently,there is a critical need to quantifiably link in-host infection pathways with the doseresponse paradigm.To better understand these relationships,we propose a new mathematical model to describe the gastro-intestinal pathway of L.monocytogenes within the host.The model dynamics are shown to be sensitive to inoculation doses and exhibit bistability phenomena.Applying the model to guinea pigs,we show how it provides useful tools to identify key parameters and to inform critical values of these parameters that are pivotal in risk evaluation.Our preliminary analysis shows that the effect of gastroenvironmental stress,the role of commensal microbiota and immune cells are critical for successful infection of L.monocytogenes and for dictating the shape of the doseresponse curves.

In-host modeling

Understanding the mechanisms governing host-pathogen kinetics is important and can guide human interventions.In-host mathematical models,together with biological data,have been used in this endeavor.In this review,we present basic models used to describe acute and chronic pathogenic infections.We highlight the power of model predictions,the role of drug therapy,and advantage of considering the dynamics of immune responses.We also present the limitations of these models due in part to the trade-off between the complexity of the model and their predictive power,and the challenges a modeler faces in determining the appropriate formulation for a given problem.

MODELING THE SCHISTOSOMIASIS ON THE ISLETS IN NANJING

A compartmental model is established for schistosomiasis infection in Qianzhou and Zimuzhou, two islets in the center of Yangtzi River near Nanjing, P. R. China. The model consists of five differential equations about the susceptible and infected subpopu- lations of mammalian Rattus norvegicus and Oncomelania snails. We calculate the basic reproductive number R0 and discuss the global stability of the disease free equilibrium and the unique endemic equilibrium when it exists. The dynamics of the model can be characterized in terms of the basic reproductive number. The parameters in the model are estimated based on the data from the field study of the Nanjing Institute of Para- sitic Diseases. Our analysis shows that in a natural isolated area where schistosomiasis is endemic, killing snails is more effective than killing Rattus norvegicus for the control of schistosomiasis.

A threshold delay model of HIV infection of newborn infants through breastfeeding

The breast milk of HIV infected women contains HIV virus particles,therefore children can become infected through breastfeeding.We develop a mathematical epidemiological model of HIV infection in infants,infected children and infected women that represents infection of an infant/child as a series of exposures,by incorporating within-host virus dynamics in the individuals exposed to the virus through breastfeeding.We show that repeated exposures of the infant/child via breastfeeding can cause bi-stability dynamics and,subsequently,infection persistence even when the epidemiological basic reproduction number R0 is less than unity.This feature of the model,due to a backward bifurcation,gives new insight into the control mechanisms of HIV disease through breastfeeding.

IDM editorial statement on the 2019-nCoV

In December of 2019,27 patients with viral pneumonia including 7 severe cases were reported inWuhan,the capital city of Hubei province and one of the largest cities of China.By the morning of January 23,2020,the infected cases have increased to 571 including 17 deaths,and spread to 25 of 31 mainland provinces and municipals and Hong Kong,Macao and Taiwan as well as to 7 other countries,including South Korea,Japan,Thailand,Singapore,Philippines,Mexico and the United States of America.