TWO-PATCH SIS STOCHASTIC MODEL: EFFECTS OF DISPERSAL RATES ON DISEASE TRANSMISSION
Abstract
Communicable diseases including measles, Covid-19 and Ebola virus can be transmitted from one community to the other through epidemic dispersal. Different dispersal mechanisms were investigated using a verity of mathematical models; however, the effect of dispersal rates on diseases transmitting between communities that differ in healthcare provisions has not been previously studied. This study, therefore, investigated such effects on the transmission of infectious diseases between two distinct patches: a community with (without) better healthcare facilities. The stochastic susceptible-infected-susceptible (SIS) model, devised through the continuous-time Markov chain (CTMC) process, together with its corresponding ordinary differential equation (ODE) model, was used to determine how changes in dispersal rates can affect the transmissions of diseases. To supplement the findings of this study, basic reproduction numbers for the two patches were also determined. We found that the dispersal rate has profound effects on the transmission of infectious diseases since increase in the dispersal rate in one community an increases the disease transmission in the other and the opposite is also true. Therefore, the transmission of diseases in not severely affected communities can be contained when travel ban is imposed in the worst affected communities.
Keywords: Continuous-time Markov Chain; Epidemic Dispersal; Gillespie Algorithm; Basic Reproduction Number
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