Disease Dynamics

Infectious diseases are transmitted either via direct contact between humans or through an intermediary vector (mosquitoes, flies, snails etc).

The questions I have been interested in how threshold behavior is influenced by factors that include seasonality and climate change, complex interactions between multiple hosts and vectors, emergent disease properties on a complex interaction networks that represent spatio-temporal heterogeneity. I am also interested in resilience of infectious diseases to perturbations that could be caused by a change in environmental or behavioral properties of hosts/vectors.


I studied these questions on models of Flu, Dengue, Visceral Leishmaniasis, Covid19, and Onchocerciasis. We reported for example non-chaoitc attractors in models of Flu assuming a quasi-periodic change in seasonality. 

Torus to chaotic dynamics as a function of seasonality. The strange nonchaotic attractor is shown (b) while torus and chaotic dynamics are in (a) and (c). The sensitivity that measures sensitive dependence on initial conditions and geometry of the attractor is shown in (d)-(f). 

A strange non-chaotic attractor in the S-I phase plane, its basin of attraction and sensitivity.


A prototypical model for studying multi-threshold dynamics in a vector borne disease. This bifurcation diagram shows backward bifurcation that occurs at R0=1 i.e. an endemic equilibrium and disease free equilibrium coexists even if R0<1. This diagram is also typical of hysteresis/memory effects in the dynamics.

Resilience

I also investigated the resilience of the disease-free and endemic states, i.e. their ability to persist under perturbation in epidemiological and ecological conditions i.e. changing vector biting preferences, additional host availability that are either competitive or dead end in the transmission dynamics.

Resilience in disease free and endemic equilibria (labeled DFE and EE) as additional dead end hosts are added in the dynamics of Visceral Leishmaniasis. The original system consisted of only humans and sandflies (black/red curve).

Spatial Heterogeneity

Complex interactions patterns arise due to interactions subject to constraints of space. Typically such systems are studied through the framework of couple systems, where the coupling could represent two or more interacting subsystems. The tools and tricks of complex network analysis are readily applied to quantify the emergent dynamical properties and their implication for disease control. 

We developed a model to study dengue transmission dynamics in a set of cities in Malaysia, that are frequented by commuters for work and other activities. An initial assessment of travel patterns gave us the following network of human interactions. We found that typical the node with more connections or the hubs are key to control with minimal effort.

The human movement network in Kedah, Malaysia (top left). Other toy networks generated out of the 11 nodes that includes small world, random and scale free configurations.

Infection on different nodes of the Kedah, Malaysia human movement network. Implementing control on a hub in the network reduces infections across other connected nodes than just targeting a node with less connectivity.

Agent-Based models

To ordinary differential equations (ODE) based models assume a homogeneous mixing between individuals and are therefore il - equipped are to account for spatial heterogeneities that exists in the real world. An individual based model or an agent based model addresses this issue by considering individuals as agents who interact with other agents via a set of rules and in the process transmit the disease. 

Currently, our group is working on an agent-based model for Covid19 in Hillsborough County, Florida, USA. This involves creating a realistic network where agents interact, a movement model based on origin-destination matrix, and a disease model. This work was made part of a dashboard at this link: http://www.seir-abm.online:8050/

Accumulation of immune individuals over time in Hillsborough county Florida in typical simulation run using an agent based model. Dots represent individuals while colors indicate simulation time.