A compartmental model for the spread of Nipah virus in a periodic environment

Nipah virus (NiV) is a zoonotic virus that causes outbreaks of fatal disease in humans. Fruit bat, also known as the flying fox, is the animal host reservoir for NiV. It is known to cause illness in pigs, which are considered an intermediate host. In this paper, we propose a model for NiV disease transmission taking into account all human-to-host animal transmission as well as the loss of immunity in those who have recovered. Furthermore, we take into consideration seasonal effects such as varying transmission rate from bats and birth rate of bats. We studied the existence and uniqueness of a disease-free -periodic solution and later deals with the basic reproduction number and stability analysis. To support the analytical results we provide numerical examples and assess the effect of parameter changes on disease dynamics, which might help to understand how to avoid a yearly periodic recurrence of the disease.</abstract

A Mathematical Model for Zika Virus Infection and Microcephaly Risk Considering Sexual and Vertical Transmission

We establish a compartmental model for Zika virus disease transmission, with particular attention paid to microcephaly, the main threat of the disease. To this end, we consider separate microcephaly-related compartments for affected infants, as well as the role of asymptomatic carriers, the influence of seasonality and transmission through sexual contact. We determine the basic reproduction number of the corresponding time-dependent model and time-constant model and study the dependence of this value on the mosquito-related parameters. In addition, we demonstrate the global stability of the disease-free periodic solution if R01. We fit our model to data from Colombia between 2015 and 2017 as a case study. The fitting is used to figure out how sexual transmission affects the number of cases among women as well as the number of microcephaly cases. Our sensitivity analyses conclude that the most effective ways to prevent Zika-related microcephaly cases are preventing mosquito bites and controlling mosquito populations, as well as providing protection during sexual contact

Global dynamics of some vector-borne infectious disease models with seasonality

Vector-borne infectious diseases such as malaria, dengue, West Nile fever, Zika fever and Lyme disease remain a threat to public health and economics. Both vector life cycle and parasite development are greatly influenced by climatic factors. Understanding the role of seasonal climate in vector-borne infectious disease transmission is particularly important in light of global warming. This PhD thesis is devoted to the study of global dynamics of four vector-borne infectious disease models. We start with a periodic vector-bias malaria model with constant extrinsic incubation period (EIP). To explore the temperature sensitivity of the EIP of malaria parasites, we also formulate a functional differential equations model with a periodic time delay. Moreover, we incorporate the use of insecticide-treated bed nets (ITNs) into a climate-based mosquito-stage-structured malaria model. Lastly, we develop a time-delayed Lyme disease model with seasonality. By using the theory of basic reproduction ratio, R0, and the theory of dynamical systems, we derive R0 and establish a threshold type result for the global dynamics in terms of R0 for each model. By conducting numerical simulations of case studies, we propose some practical strategies for the control of the diseases